Download Math 12 – Worksheet: Conic Sections Review

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Math 12 – Worksheet: Conic Sections Review
1) Identify the center and the radius for each of the following circles.
(a) ( x − 2) 2 + ( y + 4) 2 = 20
(b) 2 x 2 + 2 y 2 + 4 x − 8 y = 12
2) For each of the following ellipses, find the center and the lengths of the major and minor axes. Sketch a
graph of each ellipse.
(a)
( x + 1) 2 ( y − 3) 2
+
=1
4
6
(b) 2 x 2 + 3 y 2 − 6 x + 6 y = 12
3) For each of the following hyperbolas, find the center, vertices, and asymptotes. Sketch a graph of each
hyperbola.
(a)
( x + 5) 2 ( y − 2) 2
−
=1
6
4
(b) x 2 − y 2 + 2 x = 4 y + 17
In questions 4 – 8, identify the equation as a circle, ellipse, or hyperbola. In each case, find the center. For a
circle, find the length of the radius; for an ellipse, find the lengths of the major and minor axes; for a
hyperbola, find the coordinates of the vertices and the foci.
4) x 2 + y 2 − x + 3 y = 4
5) x 2 + 4 y 2 + 2 x − 8 y = 11
6) 3x 2 − 3 y 2 − 6 x + 12 y = 36
7) y 2 − 9 x 2 − 18 x + 6 y = 9
8) 25 x 2 + 4 y 2 − 50 x − 16 y + 1 = 60
In questions 9 – 12, write and equation in standard form for the indicated conic section.
9) Circle with center (2, 3) and radius 6
10) Ellipse with center at (5, -3); major axis of length 12; minor axis of length 10
11) Hyperbola, center at (-2, 4); transverse axis of length 8; conjugate axis of length 8; Opens up/down
12) Hyperbola, center at (-6, -5); transverse axis of length 12; conjugate axis of length 6; Opens left/right