https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:hyperb-intro/v/conic-sections-intro-to-hyperbolas 2021-03-19T16:21:24Z Intro to hyperbolas Sal introduces the standard equation for hyperbolas, and how it can be used in order to determine the direction of the hyperbola and its vertices. Sal Khan video https://cdn.kastatic.org/googleusercontent/K7U1uh1j_MEI_Mc2X2xyfTTawjdJyVbxFn2XFN_np1nCX-ly_ohMlRgH-rScJ2tOKC-gLmyJHvByWl_Ri6Mt6Tyl Intro to hyperbolas Sal introduces the standard equation for hyperbolas, and how it can be used in order to determine the direction of the hyperbola and its vertices. https://cdn.kastatic.org/ka-youtube-converted/pzSyOTkAsY4.mp4/pzSyOTkAsY4.mp4 814 Hyperbola https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/e/standard-equations-of-hyperbolas 2025-08-08T02:53:40.009522544Z Standard equations of hyperbolas Standard equations of hyperbolas Ashish Gupta exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:non-origin-hyperb/v/conic-sections-hyperbolas-3 2021-03-19T16:21:24Z Equation of a hyperbola not centered at the origin Sal analyzes the hyperbola whose equation is (x-1)^2/16-(y+1)^2/4=1, and graphs it. Sal Khan video https://cdn.kastatic.org/googleusercontent/VFpEIZ1XOiIzH_CEkT2hwpLXC2jmCAKFh4IpbsPQACXWlv0mWZezY3T-HRV9cFiYwAsZBwwUraAPZQdPIJ9UUlAt Equation of a hyperbola not centered at the origin Sal analyzes the hyperbola whose equation is (x-1)^2/16-(y+1)^2/4=1, and graphs it. https://cdn.kastatic.org/ka-youtube-converted/lGQw-W1PxBE.mp4/lGQw-W1PxBE.mp4 629 Hyperbola https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:hyperb-foci/v/foci-of-a-hyperbola 2021-03-19T16:21:24Z Foci of a hyperbola from equation Sal discusses the foci of hyperbolas and shows how they relate to hyperbola equations. Sal Khan video https://cdn.kastatic.org/googleusercontent/fN5xNEwDo7pABBo-PQVKZcs8fLgu9rFMFTSrHmvDyAHXKycHCAM8e5YS5-tCZmXF6JtwrXfVQ8WaMIHLa9rtgoo Foci of a hyperbola from equation Sal discusses the foci of hyperbolas and shows how they relate to hyperbola equations. https://cdn.kastatic.org/ka-youtube-converted/S0Fd2Tg2v7M.mp4/S0Fd2Tg2v7M.mp4 924 Hyperbola https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:hyperb-foci/e/foci-of-hyperbola-from-equation 2026-04-08T00:36:09.500768563Z Foci of a hyperbola from equation Given the equation of a hyperbola, find its foci. Sid Patel exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:hyperb-foci/e/equation_of_a_hyperbola 2026-03-24T23:41:07.080866137Z Equation of a hyperbola from features Given some features of a hyperbola, find its equation. Sid Patel exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/v/difference-of-distances-and-latus-rectum-of-hyperbola 2025-06-01T03:41:19.129224051Z Difference of distances and Latus rectum of Hyperbola In this video, we explore two key properties of the hyperbola. We'll start by reinforcing the concept that the difference of the distances from any point on the hyperbola to its two foci is a constant, equal to 2a. Then, we will define the latus rectum and derive its length formula, 2b-squared divided by a, by finding the y-coordinates of the endpoints. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Difference of distances and Latus rectum of Hyperbola In this video, we explore two key properties of the hyperbola. We'll start by reinforcing the concept that the difference of the distances from any point on the hyperbola to its two foci is a constant, equal to 2a. Then, we will define the latus rectum and derive its length formula, 2b-squared divided by a, by finding the y-coordinates of the endpoints. https://cdn.kastatic.org/ka-youtube-converted/43Am7Kth8xA.mp4/43Am7Kth8xA.mp4 285 Hyperbola https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/v/equation-of-a-hyperbola-using-its-definition 2025-06-01T03:41:19.129224051Z Equation of a hyperbola using its definition This video provides a step-by-step derivation of the standard equation of a hyperbola. We begin with its fundamental definition: the set of all points where the difference of the distances from two fixed points (the foci) is a constant (2a). Through careful algebraic steps, including squaring twice, we derive the standard equation: (x-squared / a-squared) - (y-squared / b-squared) = 1. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of a hyperbola using its definition This video provides a step-by-step derivation of the standard equation of a hyperbola. We begin with its fundamental definition: the set of all points where the difference of the distances from two fixed points (the foci) is a constant (2a). Through careful algebraic steps, including squaring twice, we derive the standard equation: (x-squared / a-squared) - (y-squared / b-squared) = 1. https://cdn.kastatic.org/ka-youtube-converted/95kvxiMNewI.mp4/95kvxiMNewI.mp4 278 Hyperbola https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/v/equation-of-a-hyperbola-using-foci-and-vertices 2025-06-01T03:41:19.129224051Z Equation of a hyperbola using foci and vertices In this video, we learn how to find the equation of a hyperbola given specific conditions related to its vertices, foci, and conjugate axis. We'll cover scenarios where the vertices and foci are given on either the x-axis or y-axis, and also when the foci and the length of the conjugate axis are provided, to determine the values of 'a' and 'b' and write the hyperbola's standard equation. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of a hyperbola using foci and vertices In this video, we learn how to find the equation of a hyperbola given specific conditions related to its vertices, foci, and conjugate axis. We'll cover scenarios where the vertices and foci are given on either the x-axis or y-axis, and also when the foci and the length of the conjugate axis are provided, to determine the values of 'a' and 'b' and write the hyperbola's standard equation. https://cdn.kastatic.org/ka-youtube-converted/0RwYA78gHP0.mp4/0RwYA78gHP0.mp4 211 Hyperbola https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/v/equation-of-a-hyperbola-using-eccentricity-and-latus-rectum 2025-06-01T03:41:19.129224051Z Equation of a hyperbola using eccentricity and latus rectum This video demonstrates how to find the equation of a hyperbola using diverse conditions such as its foci and the length of its latus rectum, or its vertices and eccentricity. We also tackle a problem where the foci are given and the hyperbola passes through a specific point, requiring solving for 'a squared' and 'b squared' by setting up and solving relevant equations. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of a hyperbola using eccentricity and latus rectum This video demonstrates how to find the equation of a hyperbola using diverse conditions such as its foci and the length of its latus rectum, or its vertices and eccentricity. We also tackle a problem where the foci are given and the hyperbola passes through a specific point, requiring solving for 'a squared' and 'b squared' by setting up and solving relevant equations. https://cdn.kastatic.org/ka-youtube-converted/II15ScY1hrE.mp4/II15ScY1hrE.mp4 361 Hyperbola https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/e/equation-of-a-hyperbola-using-eccentricity-and-latus-rectum 2025-08-08T02:53:40.009522544Z Equation of a hyperbola using eccentricity and latus rectum Equation of a hyperbola using eccentricity and latus rectum Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/v/finding-parts-of-a-hyperbola-given-the-equation 2025-06-01T03:41:19.129224051Z Finding parts of a hyperbola given the equation This video focuses on finding the essential characteristics of a hyperbola from its equation. We will determine the coordinates of the foci and vertices, the eccentricity, and the length of the latus rectum. We'll work through examples like (x squared divided by 16) minus (y squared divided by 9) equals 1, and cases where the transverse axis is along the y-axis, such as 5y squared minus 9x squared equals 36. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding parts of a hyperbola given the equation This video focuses on finding the essential characteristics of a hyperbola from its equation. We will determine the coordinates of the foci and vertices, the eccentricity, and the length of the latus rectum. We'll work through examples like (x squared divided by 16) minus (y squared divided by 9) equals 1, and cases where the transverse axis is along the y-axis, such as 5y squared minus 9x squared equals 36. https://cdn.kastatic.org/ka-youtube-converted/VhE32b-CH9E.mp4/VhE32b-CH9E.mp4 266 Hyperbola https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/e/finding-parts-of-a-hyperbola-given-the-equation-1 2025-08-08T02:53:40.009522544Z Finding parts of a hyperbola given the equation Finding parts of a hyperbola given the equation Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:hyperbola/e/equation-of-a-hyperbola-passing-through-a-given-point 2025-08-08T02:53:40.009522544Z Equation of a hyperbola passing through a given point Equation of a hyperbola passing through a given point Ashish Gupta exercise