Download Worksheet 5 Circles, Parabolas and Ellipses Review Find the

Worksheet 5
Circles, Parabolas and Ellipses Review
Find the standard form of the conic section with given characteristics.
1
Circle with endpoints of a diameter at ( −1, 2 ) and ( 5, 6 ) .
Parabola with vertex at ( 4, 2 ) and focus at ( 4, 0 ) .
2
Ellipse with vertices ( 0, ±6 ) and passing through the point ( 2, 2 ) .
3
Ellipse with vertices at ( 2, 0 ) and ( 2, 4 ) and foci at ( 2,1) and ( 2, 3) .
4
Identify the conic section. Write the equation in standard form.
5
4x 2 + 4y 2 + 32x24y + 51 = 0
6
4x 2 + 25y 2 + 16x − 150y + 141 = 0
7
Find the x- and y-intercepts of the graph of the circle: ( x + 5 ) + ( y − 6 ) = 27
8
Find the x- and y-intercepts of the graph of the parabola: ( x − 2 ) = 4 ( y + 3)
2
2
2
9
Sketch a complete graph of the ellipse:
( x − 4 )2 ( y + 4 )2
6
+
9
= 1 . Identify the center, vertices, foci and eccentricity of
the ellipse.
Sketch a complete graph of the parabola: ( y − 1) = −8 ( x + 3) . Identify the vertex, focus and directrix.
10
2
Answers
1. ( x − 2 ) + ( y − 4 ) = 13
2
4.
2
( x − 2 )2 ( y − 2 )2
(
3
+
)
4
=1
7. 3 ± 6, 0 ; no y-intercepts
2.
( x − 4 )2 = −8 ( y − 2 )
3.
5. Circle; ( x + 4 ) + ( y − 3) =
2
(
)
8. 2 ± 2 3, 0 ; ( 0, −2 )
2
99
4
6.
x 2 y2
+
=1
9
36
2
( x + 2 )2 ( y − 3)2
25
+
4
=1