https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/applications-of-parabolas 2025-06-01T03:41:19.129224051Z Applications of parabolas In this video, we explore practical applications of parabolas. We'll solve a problem involving a parabolic mirror, determining its width at a certain depth given the location of its focus. We'll also analyze a deflected beam, shaped like a parabola, to find how far from the centre the deflection is a specific amount, by first finding the equation of the parabola. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Applications of parabolas In this video, we explore practical applications of parabolas. We'll solve a problem involving a parabolic mirror, determining its width at a certain depth given the location of its focus. We'll also analyze a deflected beam, shaped like a parabola, to find how far from the centre the deflection is a specific amount, by first finding the equation of the parabola. https://cdn.kastatic.org/ka-youtube-converted/UF6vKvRGjiY.mp4/UF6vKvRGjiY.mp4 410 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/applications-of-parabolas 2025-08-08T02:53:40.009522544Z Applications of parabolas Applications of parabolas Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/applications-of-ellipses 2025-06-01T03:41:19.129224051Z Applications of ellipses This video showcases real-world applications of ellipses. We'll calculate the height of a semi-elliptical arch at a specific point from one end, given its overall width and height. We'll also determine the equation of the elliptical path traced by a man running such that the sum of his distances from two fixed flag posts remains constant. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Applications of ellipses This video showcases real-world applications of ellipses. We'll calculate the height of a semi-elliptical arch at a specific point from one end, given its overall width and height. We'll also determine the equation of the elliptical path traced by a man running such that the sum of his distances from two fixed flag posts remains constant. https://cdn.kastatic.org/ka-youtube-converted/uF6Ow2YmPys.mp4/uF6Ow2YmPys.mp4 451 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/applications-of-ellipses 2025-08-08T02:53:40.009522544Z Applications of ellipses Applications of ellipses Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/triangles-inscribed-inside-parabolas 2025-06-01T03:41:19.129224051Z Triangles inscribed inside parabolas In this video, we solve geometric problems involving triangles inscribed within parabolas. First, we find the area of a triangle formed by joining the vertex of a parabola (like x-squared equals 12y) to the endpoints of its latus rectum. Second, we determine the length of the side of an equilateral triangle inscribed in the parabola y-squared equals 4ax, where one vertex of the triangle is at the vertex of the parabola. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Triangles inscribed inside parabolas In this video, we solve geometric problems involving triangles inscribed within parabolas. First, we find the area of a triangle formed by joining the vertex of a parabola (like x-squared equals 12y) to the endpoints of its latus rectum. Second, we determine the length of the side of an equilateral triangle inscribed in the parabola y-squared equals 4ax, where one vertex of the triangle is at the vertex of the parabola. https://cdn.kastatic.org/ka-youtube-converted/VoxK1C4Sk9E.mp4/VoxK1C4Sk9E.mp4 324 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/triangles-inscribed-inside-parabolas 2025-08-08T02:53:40.009522544Z Triangles inscribed inside parabolas Triangles inscribed inside parabolas Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/finding-the-locus-of-a-moving-point 2025-06-01T03:41:19.129224051Z Finding the locus of a moving point This video explains how to find the equation of the locus of a moving point under specific geometric conditions. We'll work through a problem where a rod of a given length rests between the coordinate axes, and a point P is taken on the rod at a fixed distance from one end. By parameterizing the coordinates of P using an angle and then eliminating the angle, we show that its locus is an ellipse. A similar second example is also discussed. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding the locus of a moving point This video explains how to find the equation of the locus of a moving point under specific geometric conditions. We'll work through a problem where a rod of a given length rests between the coordinate axes, and a point P is taken on the rod at a fixed distance from one end. By parameterizing the coordinates of P using an angle and then eliminating the angle, we show that its locus is an ellipse. A similar second example is also discussed. https://cdn.kastatic.org/ka-youtube-converted/WNEi1qvBOIY.mp4/WNEi1qvBOIY.mp4 360 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/finding-the-locus-of-a-moving-point 2025-08-08T02:53:40.009522544Z Finding the locus of a moving point Finding the locus of a moving point Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/equation-of-a-circle-between-a-line-and-the-axes 2025-06-01T03:41:19.129224051Z Equation of a circle between a line and the axes In this video, we tackle the problem of finding the equations of all circles that touch both coordinate axes and a given straight line (for example, 3x minus 4y plus 8 equals 0). We'll consider the possible locations of the circle's centre in different quadrants (like (a, a) or (-a, a) with radius 'a') and use the condition that the perpendicular distance from the centre to the given line must be equal to the radius. This leads to solving equations involving absolute values to find possible radii and centres. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of a circle between a line and the axes In this video, we tackle the problem of finding the equations of all circles that touch both coordinate axes and a given straight line (for example, 3x minus 4y plus 8 equals 0). We'll consider the possible locations of the circle's centre in different quadrants (like (a, a) or (-a, a) with radius 'a') and use the condition that the perpendicular distance from the centre to the given line must be equal to the radius. This leads to solving equations involving absolute values to find possible radii and centres. https://cdn.kastatic.org/ka-youtube-converted/6iuhZbY3Vkc.mp4/6iuhZbY3Vkc.mp4 484 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/equation-of-a-circle-between-a-line-and-the-axes 2025-08-08T02:53:40.009522544Z Equation of a circle between a line and the axes Equation of a circle between a line and the axes Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/equation-of-a-circle-touching-another-circle 2025-06-01T03:41:19.129224051Z Equation of a circle touching another circle This video explores scenarios involving circles touching other circles. We'll find the equation of a circle with a given radius that touches another specified circle externally at a given point. We also determine the point of contact when two circles touch externally. Finally, we find the equation of a circle that touches another internally at a point, with the condition that the new circle's centre lies on the x-axis, using the collinearity of centres and the point of contact. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of a circle touching another circle This video explores scenarios involving circles touching other circles. We'll find the equation of a circle with a given radius that touches another specified circle externally at a given point. We also determine the point of contact when two circles touch externally. Finally, we find the equation of a circle that touches another internally at a point, with the condition that the new circle's centre lies on the x-axis, using the collinearity of centres and the point of contact. https://cdn.kastatic.org/ka-youtube-converted/W1Qehy4MoRk.mp4/W1Qehy4MoRk.mp4 403 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/equation-of-a-circle-touching-another-circle 2025-08-08T02:53:40.009522544Z Equation of a circle touching another circle Equation of a circle touching another circle Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/equation-of-a-circle-given-centre-and-length-of-a-chord 2025-06-01T03:41:19.129224051Z Equation of a circle given centre and length of a chord In this video, we solve problems related to circles and chords. First, we find the equation of a circle given its centre and the length of a chord it cuts off on a specific line. Then, we determine the length of a chord intercepted by a given circle on a given line. Lastly, we find the equations of lines parallel to a given line that cut off a chord of a specific length from a given circle. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of a circle given centre and length of a chord In this video, we solve problems related to circles and chords. First, we find the equation of a circle given its centre and the length of a chord it cuts off on a specific line. Then, we determine the length of a chord intercepted by a given circle on a given line. Lastly, we find the equations of lines parallel to a given line that cut off a chord of a specific length from a given circle. https://cdn.kastatic.org/ka-youtube-converted/sqzeBeuz_VA.mp4/sqzeBeuz_VA.mp4 469 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/equation-of-a-circle-given-centre-and-length-of-a-chord 2025-08-08T02:53:40.009522544Z Equation of a circle given centre and length of a chord Equation of a circle given centre and length of a chord Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/v/equation-of-conic-sections-using-definitions 2025-06-01T03:41:19.129224051Z Equation of conic sections using definitions In this video, we derive the equations of conic sections directly from their fundamental locus definitions. We'll find the equation for the set of points where the sum of distances from two fixed points is constant (an ellipse). We'll also find the equation for points where the distance from a fixed point is a constant fraction (eccentricity) of the distance from a fixed line (a general conic, in this case an ellipse). Finally, we'll show that the set of points where the difference of distances from two fixed points is constant represents a hyperbola. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of conic sections using definitions In this video, we derive the equations of conic sections directly from their fundamental locus definitions. We'll find the equation for the set of points where the sum of distances from two fixed points is constant (an ellipse). We'll also find the equation for points where the distance from a fixed point is a constant fraction (eccentricity) of the distance from a fixed line (a general conic, in this case an ellipse). Finally, we'll show that the set of points where the difference of distances from two fixed points is constant represents a hyperbola. https://cdn.kastatic.org/ka-youtube-converted/28q5KdEj8kU.mp4/28q5KdEj8kU.mp4 429 Applications of conic sections https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:applications-of-conic-sections/e/equation-of-conic-sections-using-definitions 2025-08-08T02:53:40.009522544Z Equation of conic sections using definitions Equation of conic sections using definitions Ashish Gupta exercise