Ellipses: Standard Form - Video Tutorials & Practice Problems
Graph Ellipses at Origin
Video transcript
Given the equation 4x2+9y2=1, sketch a graph of the ellipse.
Given the ellipse equation 16x2+4y2=1, determine the magnitude of the semi-major axis (a) and the semi-minor axis (b).
a=16, b=4
a=4, b=16
a=4, b=2
a=2, b=4
Foci and Vertices of an Ellipse
Video transcript
Determine the vertices and foci of the following ellipse: 49x2+36y2=1.
Vertices: (7,0),(−7,0)
Foci: (6,0),(−6,0)
Vertices: (6,0),(−6,0)
Foci: (7,0),(−7,0)
Vertices: (7,0),(−7,0)
Foci: (13,0),(−13,0)
Vertices: (0,7),(0,−7)
Foci: (0,13),(0,−13)
Determine the vertices and foci of the following ellipse: 9x2+16y2=1.
Vertices: (4,0),(−4,0)
Foci: (7,0),(−7,0)
Vertices: (0,4),(0,−4)
Foci: (0,7),(0,−7)
Vertices: (4,0),(−4,0)
Foci: (3,0),(−3,0)
Vertices: (0,4),(0,−4)
Foci: (0,3),(0,−3)
Find the standard form of the equation for an ellipse with the following conditions.
Foci = (−5,0),(5,0)
Vertices = (−8,0),(8,0)
64x2+25y2=1
25x2+64y2=1
8x2+5y2=1
64x2+39y2=1
Graph Ellipses NOT at Origin
Video transcript
Graph the ellipse .
Determine the vertices and foci of the ellipse (x+1)2+4(y−2)2=1.
Vertices: (−1,4),(−1,0)
Foci: (−1,2+3),(−1,2−3)
Vertices: (−1,4),(−1,0)
Foci: (−2,2),(0,2)
Vertices: (−2,2),(0,2)
Foci: (1,2+3),(1,2−3)
Vertices: (−2,2),(0,2)
Foci: (2+3,1),(2−3,1)
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- Graph the ellipse and locate the foci. (y^2)/25 + (x^2)/16 = 1
- Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (-4,0), (4,0); Ve...
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- Graph the ellipse and locate the foci. 9x^2 + 4y^2 - 18x + 8y -23 = 0
- In Exercises 1–18, graph each ellipse and locate the foci. x^2/16 +y^2/4 = 1
- Graph the ellipse and locate the foci. (x^2)/36 +(y^2)/25 = 1
- In Exercises 1–18, graph each ellipse and locate the foci. x^2/9 +y^2/36= 1
- In Exercises 1–18, graph each ellipse and locate the foci. x^2/25 +y^2/64 = 1
- In Exercises 1–18, graph each ellipse and locate the foci. x^2/49 +y^2/81 = 1
- In Exercises 1–18, graph each ellipse and locate the foci. x^2/(9/4) +y^2/(25/4) = 1
- In Exercises 1–18, graph each ellipse and locate the foci. x² = 1 – 4y²
- In Exercises 1–18, graph each ellipse and locate the foci. 25x²+4y² = 100
- In Exercises 1–18, graph each ellipse and locate the foci.4x²+16y² = 64
- In Exercises 1–18, graph each ellipse and locate the foci. 7x² = 35-5y²
- In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci.
- In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci.
- In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci.
- In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Fo...
- In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Fo...
- In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Fo...
- In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Ma...
- In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Ma...
- In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 2)²/9 + (y -1)² /4= 1
- In Exercises 37–50, graph each ellipse and give the location of its foci. (x +3)²+ 4(y -2)² = 16
- In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 4)²/9 + (y +2)² /25= 1
- In Exercises 37–50, graph each ellipse and give the location of its foci. x²/25 + (y -2)² /36= 1
- In Exercises 37–50, graph each ellipse and give the location of its foci. (x +3)²/9 + (y -2)² = 1
- In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 1)²/2 + (y +3)² /5= 1
- In Exercises 49–56, identify each equation without completing the square. 4x^2 - 9y^2 - 8x - 36y - 68 = 0
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- In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the...
- In Exercises 51–60, convert each equation to standard form by completing the square on x and y. Then graph the...
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