Pre-AP PreCalculus Test Review Conic Sections 1 – 13 are due before you leave class. 1-4: For the given equations complete the following: a) Identify the type of conic section, b) Write the equation of the conic section in standard form, c) List all of the important features of the conic section, d) Sketch a graph of the conic section (be sure to include all of the important features). 1) 9𝑥 2 + 16𝑦 2 + 18𝑥 − 64𝑦 = 71 2) 𝑥 2 − 16𝑦 2 − 2𝑥 + 128𝑦 − 271 = 0 3) 2𝑥 2 + 2𝑦 2 − 8𝑥 + 4𝑦 − 8 = 0

4) 3𝑥 2 + 12𝑥 + 𝑦 + 12 = 2

7-8: Write the equation of the conic section in standard form using the information given below: 5) A circle with center at (−4, 2) and a point on the circle of (3, −1). 6) A hyperbola with a center at (2, 1), vertex at (2, 4), and a focus at (2, 6).

7) A parabola with vertex at (2, 3) and a focus at (2, 2).

8) An ellipse with foci at (1, 0) and (−1, 0) and minor axis of length of 4.

9-12: Graph the conic section. 9)

(𝑦+6)2 64

−

(𝑥−3)2 35

=1

11) (𝑥 − 5)2 = 12(𝑦 + 4)

10)

(𝑥+2)2 16

+

(𝑦−1)2 36

=1

12) (𝑥 − 2)2 + 𝑦 2 = 100

13-21: Identify the conic, put it in standard form, and identify the important characteristics. 13) −3𝑥 2 − 24𝑥 + 𝑦 − 40 = 8 14) 25𝑥 2 + 16𝑦 2 + 150𝑥 − 160𝑦 + 225 = 0 15) 𝑦 2 − 9𝑥 2 + 36𝑥 − 8𝑦 − 20 = 9 16) 4𝑥 2 + 9𝑦 2 = 36

18) 2𝑥 2 − 4𝑥 − 𝑦 − 2 = −3

20) 2𝑥 2 + 2𝑦 2 + 20𝑥 − 8𝑦 + 38 = −2

17) 𝑥 2 + 9𝑦 2 + 2𝑥 − 18𝑦 − 7 = 1 19) 𝑥 2 − 3𝑦 2 + 6𝑦 − 4 = 1

22-29: Write the equation in standard form given the following information. 21) An ellipse with foci at (−5, 1) and (3, 1) and major vertex at (11, 1). 22) A circle with center at (5, −1) and radius of 4. 23) A hyperbola with foci at (3, 1) and (3, −5) and a vertex at (3, 0). 24) A parabola with vertex at (−1, 4), focus at (−1, 6).