https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/v/conic-sections-intro-to-ellipses 2023-07-27T01:47:53.920337803Z Intro to ellipses Learn all about ellipses in this video. The standard form for an ellipse centered at the origin is x²/a² + y²/b² = 1. The semi-major axis is the longest radius and the semi-minor axis is the shortest radius. The video also explains how to shift an ellipse. Sal Khan video https://cdn.kastatic.org/googleusercontent/D5XS31KtD3HUL7SHsmzd_JIMx34-i0GpaT_aO8lkQ9ZJ-xQh8o_aqjYRbOoOi1pxn3PrusQB7Bl6CSkBWjBjmBHT Intro to ellipses Learn all about ellipses in this video. The standard form for an ellipse centered at the origin is x²/a² + y²/b² = 1. The semi-major axis is the longest radius and the semi-minor axis is the shortest radius. The video also explains how to shift an ellipse. https://cdn.kastatic.org/ka-youtube-converted/lvAYFUIEpFI.mp4/lvAYFUIEpFI.mp4 854 Ellipse https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/v/ellipse-graph-from-standard-equation 2023-07-27T01:47:53.920337803Z Ellipse graph from standard equation This video explains how to graph an ellipse when given its equation in standard form. The center of this ellipse is (4,1), the horizontal radius is 4, and the vertical radius is 7. The key definitions are center, horizontal radius, and vertical radius. video https://cdn.kastatic.org/ka_thumbnails_cache/29648efc-ac54-49e4-b845-3eb93ca9bca5_1280_720_base.png Ellipse graph from standard equation This video explains how to graph an ellipse when given its equation in standard form. The center of this ellipse is (4,1), the horizontal radius is 4, and the vertical radius is 7. The key definitions are center, horizontal radius, and vertical radius. https://cdn.kastatic.org/ka-youtube-converted/h5dIVNjVjXg.mp4/h5dIVNjVjXg.mp4 100 Ellipse https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/v/ellipse-standard-equation-from-graph 2022-10-07T00:22:18.752150461Z Ellipse standard equation from graph Given an ellipse on the coordinate plane, Sal finds its standard equation, which is an equation in the form (x-h)²/a²+(y-k)²/b²=1. video https://cdn.kastatic.org/ka_thumbnails_cache/a3aaad6a-5935-4879-b8ea-9444c7e150f1_1280_720_base.png Ellipse standard equation from graph Given an ellipse on the coordinate plane, Sal finds its standard equation, which is an equation in the form (x-h)²/a²+(y-k)²/b²=1. https://cdn.kastatic.org/ka-youtube-converted/_JrQF8Rkaio.mp4/_JrQF8Rkaio.mp4 215 Ellipse https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/e/equation_of_an_ellipse 2025-03-01T15:52:37.13987578Z Center & radii of ellipses from equation Find the center and major and minor radius of an ellipse given its equation. Sid Patel exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/e/center-and-radii-of-an-ellipse-and-its-graph 2026-04-08T00:16:02.937952483Z Graph & features of ellipses Find the center and radii of an ellipse from its graph, and vice versa. Sid Patel exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/a/ellipse-features-review 2024-10-16T19:37:28.253855216Z Ellipse features review Review all the features of an ellipse: center, vertices, co-vertices, major radius, minor radius, and foci. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-foci/v/foci-of-an-ellipse 2021-03-19T16:21:24Z Foci of an ellipse from equation Sal explains how the radii and the foci of an ellipse relate to each other, and how we can use this relationship in order to find the foci from the equation of an ellipse. Sal Khan video https://cdn.kastatic.org/googleusercontent/Yz3g-FK-xyNlN0n9dnHPMLLICOGJjZ5vDhj2O6XmMgEDGMPOCwhfkz3GQlfRXITSUoq5mMNqlfllza9EQyRdjwGANA Foci of an ellipse from equation Sal explains how the radii and the foci of an ellipse relate to each other, and how we can use this relationship in order to find the foci from the equation of an ellipse. https://cdn.kastatic.org/ka-youtube-converted/QR2vxfwiHAU.mp4/QR2vxfwiHAU.mp4 829 Ellipse https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-foci/e/find-foci-of-ellipse-from-radii 2026-04-08T00:54:09.631945657Z Foci of an ellipse from radii Given the major and minor radii of an ellipse, find its foci. Sid Patel exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/e/equation-of-an-ellipse-from-its-graph 2026-04-08T00:16:02.937952483Z Ellipse standard equation & graph Given the graph of an ellipse, find its equation, and vice versa. Sid Patel exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-center-radii/a/ellipse-equation-review 2024-10-16T19:37:28.253855216Z Ellipse equation review Review your knowledge of ellipse equations and their features: center, radii, and foci. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:conics/x9e81a4f98389efdf:ellipse-foci/e/foci-of-ellipse-from-equation 2025-03-01T15:52:37.13987578Z Foci of an ellipse from equation Given the equation of an ellipse, find its foci. Sid Patel exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:ellipse/v/eccentricity-and-latus-rectum-of-an-ellipse 2025-06-01T03:41:19.129224051Z Eccentricity and latus rectum of an Ellipse In this video, we focus on two important properties of an ellipse: its eccentricity and its latus rectum. We'll define eccentricity as the ratio of the distance from the centre to a focus (c) to the distance from the centre to a vertex (a). We will also derive the formula for the length of the latus rectum and explain what it represents geometrically. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Eccentricity and latus rectum of an Ellipse In this video, we focus on two important properties of an ellipse: its eccentricity and its latus rectum. We'll define eccentricity as the ratio of the distance from the centre to a focus (c) to the distance from the centre to a vertex (a). We will also derive the formula for the length of the latus rectum and explain what it represents geometrically. https://cdn.kastatic.org/ka-youtube-converted/nBKUiiha2CM.mp4/nBKUiiha2CM.mp4 302 Ellipse https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:ellipse/v/equation-of-an-ellipse-using-its-definition 2025-06-01T03:41:19.129224051Z Equation of an ellipse using its definition This video provides a step-by-step derivation of the standard equation of an ellipse from its fundamental definition. We start with the condition that for any point on the ellipse, the sum of its distances from two fixed points (the foci) is a constant (2a). Through careful algebraic manipulation, including squaring both sides twice, we derive the familiar equation: (x-squared / a-squared) + (y-squared / b-squared) = 1. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of an ellipse using its definition This video provides a step-by-step derivation of the standard equation of an ellipse from its fundamental definition. We start with the condition that for any point on the ellipse, the sum of its distances from two fixed points (the foci) is a constant (2a). Through careful algebraic manipulation, including squaring both sides twice, we derive the familiar equation: (x-squared / a-squared) + (y-squared / b-squared) = 1. https://cdn.kastatic.org/ka-youtube-converted/yVXxnPBWVao.mp4/yVXxnPBWVao.mp4 337 Ellipse https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:ellipse/v/finding-parts-of-an-ellipse-given-the-equation 2025-06-01T03:41:19.129224051Z Finding parts of an ellipse given the equation In this video, we focus on identifying key characteristics of an ellipse from its standard equation. We'll find the coordinates of the foci and vertices, lengths of the major and minor axes, the eccentricity, and the length of the latus rectum. We'll work through examples where the major axis is horizontal, like (x squared by 36) + (y squared by 16) = 1, and where it's vertical, like (x squared by 4) + (y squared by 25) = 1. We also explain how to derive the latus rectum formula. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding parts of an ellipse given the equation In this video, we focus on identifying key characteristics of an ellipse from its standard equation. We'll find the coordinates of the foci and vertices, lengths of the major and minor axes, the eccentricity, and the length of the latus rectum. We'll work through examples where the major axis is horizontal, like (x squared by 36) + (y squared by 16) = 1, and where it's vertical, like (x squared by 4) + (y squared by 25) = 1. We also explain how to derive the latus rectum formula. https://cdn.kastatic.org/ka-youtube-converted/Amp962c01is.mp4/Amp962c01is.mp4 601 Ellipse https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:ellipse/e/finding-parts-of-an-ellipse-given-the-equation 2025-08-08T02:53:40.009522544Z Finding parts of an ellipse given the equation Finding parts of an ellipse given the equation Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:ellipse/v/finding-equation-of-an-ellipse 2025-06-01T03:41:19.129224051Z Finding equation of an ellipse This video explains how to determine the equation of an ellipse based on various given properties. We'll cover cases where vertices and foci are provided, where the ends of the major and minor axes are known, where the length of the major or minor axis along with foci are given, and scenarios involving the values of 'a', 'b', or 'c'. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding equation of an ellipse This video explains how to determine the equation of an ellipse based on various given properties. We'll cover cases where vertices and foci are provided, where the ends of the major and minor axes are known, where the length of the major or minor axis along with foci are given, and scenarios involving the values of 'a', 'b', or 'c'. https://cdn.kastatic.org/ka-youtube-converted/EwWfvweP6Pc.mp4/EwWfvweP6Pc.mp4 436 Ellipse https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:ellipse/v/equation-of-an-ellipse-passing-through-given-points 2025-06-01T03:41:19.129224051Z Equation of an ellipse passing through given points In this video, we learn how to find the equation of an ellipse when its centre is at the origin, the orientation of its major axis is known (either x-axis or y-axis), and it passes through two given points. We'll set up a system of equations using the standard ellipse form and the coordinates of the points to solve for 'a squared' and 'b squared', and then write the ellipse's equation. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Equation of an ellipse passing through given points In this video, we learn how to find the equation of an ellipse when its centre is at the origin, the orientation of its major axis is known (either x-axis or y-axis), and it passes through two given points. We'll set up a system of equations using the standard ellipse form and the coordinates of the points to solve for 'a squared' and 'b squared', and then write the ellipse's equation. https://cdn.kastatic.org/ka-youtube-converted/H707Bm9BmCQ.mp4/H707Bm9BmCQ.mp4 257 Ellipse https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:conic-sections-ncert-new/x0419e5b3b578592a:ellipse/e/ellipse-passing-through-given-points-8 2025-08-08T02:53:40.009522544Z Equation of an ellipse passing through given points plan: Equation of an ellipse passing through given points Ashish Gupta exercise