Ellipse Worksheet #2
#1:
(𝑥)2
25
+
(𝑦)2
36
=1
Center:
Vertices:
Co-Vertices:
Foci:
Length of Major Axis:
Length of Minor Axis:
#2:
(𝑥−3)2
25
+
(𝑦+2)2
49
=1
Center:
Vertices:
Co-Vertices:
Foci:
Length of Major Axis:
Length of Minor Axis:
#3:
(𝑥+1)2
36
+
(𝑦+4)2
9
=1
Center:
Vertices:
Co-Vertices:
Foci:
Length of Major Axis:
Length of Minor Axis:
#4:
4(𝑥 − 1)2 + 16(𝑦 + 2)2 = 64
Center:
Vertices:
Co-Vertices:
Foci:
#6. Graph the ellipse and find all of the required information: 36𝑥 2 + 𝑦 2 + 288𝑥 − 2𝑦 + 541 = 0
Center:
Vertices:
Co-Vertices:
Foci:
#7. Graph the ellipse and find all of the required information.
4𝑥 2 + 49𝑦 2 + 294𝑦 + 245 = 0
Center:
Vertices:
Co-Vertices:
Foci:
#8. Graph the ellipse and find all of the required information.
9𝑥 2 + 4𝑦 2 − 36𝑥 + 48𝑦 + 144 = 0
Center:
Vertices:
Co-Vertices:
Foci:
#9. Write the equation of the ellipse whose major axis has endpoints (6, 4) and
(-2, 4) and whose minor axis has a length of 6 units.
#10. Write the equation of the ellipse with co-vertices located at (-3, 8)
and (-3, 2) and a focus located at (4, 5).
#11. Write the equation of the ellipses that matches the graphs shown.
#12. Write an equation of an ellipse that has a center of (-6, 9), the major axis is 18 units long, and the minor axis is 8 units long.
The major axis is horizontal.
#13. Write an equation of an ellipse that has a center of (-6, -8), the major axis is 20 units long, and the minor axis is 2 units long.
The minor axis is horizontal.
#14. Write an equation of an ellipse that has a center of (4, 7), the major axis is 24 units long, and the minor axis is 20 units long.
The major axis is horizontal.
#15. Find the equation of the ellipse if given the center (-2, -9), vertex (-7, -9), and focus (-5, -9).
#16. Find the equation of the ellipse if given the center (4, 4), vertex (4, -10), and focus (4, 4 + 6√5).
17.
Use the information provided to write the equation of the ellipse being described in each scenario.
Major axis is vertical, Center: (10, -9), minor axis is 12 units long, major axis is 10 units long.
18. Write the equation of a circle that is tangent to the line x = 4 that has a center (-3, 8).
55
, 9) and
8
19. Write the equation of the parabola that has a focus of (
a directrix of 𝑥 =
57
.
8
20. Write the equation of the parabola who’s general equation is 2𝑥 2 + 32𝑥 + 𝑦 + 135 = 0
ANSWERS