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PRACTICE ON ELLIPSES (6.3)
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AM(1)
1. REMEMBER - QUEST (75-ish points) on WEDNESDAY on 6.1 - 6.3
2. Given the equation 4x 2 + 25y2 = 100 , find the center, the coordinates of the 4 vertices and
the coordinates of the foci.
3. Given the equation 4(x − 7)2 + 25(y + 2)2 = 100 , find, find the center, the coordinates of the 4
vertices and the coordinates of the foci.
4. Find the equation of an ellipse centered at (3, -1) with minor axis length 8 and one vertex of
the major axis at (3, 10). Find the coordinates of the foci as well.
5 Find the center, vertices, and foci of the following ellipse. 3x 2 − 24x + 9y 2 + 18y + 30 = 0
6. Find the equation of an ellipse and the foci the same ellipse with center (0, 0),
vertices ( ± 7, 0), and endpoint of the minor axis (0, ± 2).
7. Find the equation and foci of an ellipse with center (0, 0), y-intercepts ± 4, and major axis
length 12.
8. Sketch the following ellipse and label x and y intercepts and foci. 9x 2 + 16y 2 = 144
9. Determine all values of x so that the distance between A(1, 3) and B (2x, – 5) is 10.
10. Consider the circle with equation x 2 + 10x + y2 − 2y = 10 . Give equations for the following
lines.
a) A line that is parallel to the y-axis and tangent to the circle.
b) Line that is tangent to the circle and has inclination 45º.
11. Find the equation of an ellipse with center at the origin one vertex at (0, -9) and minor axis
6 units long. Find the coordinates of the foci as well.
12. Find the equation of an ellipse centered at (1, 2) with minor axis length 10 and one vertex
of the major axis at (8, 2). Find the coordinates of the foci as well.
13.
Find the equation of an ellipse with center (0, 0), minor axis length 8, foci (0, 5) and (0, -5).
14. Find the center, vertices, and foci of the following ellipse.
9x 2 + y 2 + 18x − 6y + 9 = 0
*** 15. Find the equation of an ellipse with center (3, 7) one focus at (6, 7), one vertex and (8, 7).
Make sure to sketch
*** 16. Find the equation of an ellipse with center (4, -1), one vertex at (4, -5), and one focus at
(4, -3.5).
17. Sketch. Find the vertices, endpoints of the minor axis, and foci.
(x − 3)2 ( y + 1))2
2
2
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x + 9y = 36 !!
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25
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18. Find the equation of an ellipse with center (0, 0), major axis length 20, foci ( ±5 3 , 0)!
19. Find the equation of the following ellipses.
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b)