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Placement Test Practice — Conic Sections
Placement Test Practice — Conic Sections
Practice Test — 20 Questions
1. Find the center and radius: $(x-4)^2+(y+1)^2=36$.
2. Find vertex and focus: $x^2 = 20y$.
3. Find vertices: $\frac{x^2}{36}+\frac{y^2}{16}=1$.
4. Find asymptotes: $\frac{x^2}{25}-\frac{y^2}{9}=1$.
5. Classify: $3x^2+3y^2 = 27$.
6. Classify: $x^2-4y^2+2x+16y-11=0$.
7. Find foci: $\frac{x^2}{169}+\frac{y^2}{144}=1$.
8. Write equation: parabola, vertex $(0,0)$, focus $(2,0)$.
9. Find $c$: $\frac{x^2}{4}-\frac{y^2}{5}=1$.
10. Eccentricity: $\frac{x^2}{25}+\frac{y^2}{16}=1$.
11. Complete the square: $x^2+y^2-4x+10y+20=0$.
12. Classify: $y^2 = 8x$.
13. What shape has equal $a$ and $b$?
14. A hyperbola's $e$ is always ___ 1.
15. Find $b$: ellipse with $a = 10$, $c = 6$.
16. Directrix of $x^2 = -16y$?
17. Write equation: circle, center $(3,-2)$, through $(6,2)$.
18. Vertices of $\frac{y^2}{9}-\frac{x^2}{4}=1$?
19. Major axis length: $\frac{x^2}{81}+\frac{y^2}{49}=1$?
20. Discriminant of $2x^2+3xy-2y^2=5$?
Show Answer Key
1. Center $(4,-1)$, $r = 6$
2. Vertex $(0,0)$, $p=5$, focus $(0,5)$
3. $(\pm 6, 0)$
4. $y = \pm \frac{3}{5}x$
5. Circle ($A=C=3$)
6. Hyperbola (opposite signs on squared terms)
7. $c = \sqrt{169-144} = 5$; foci $(\pm 5, 0)$
8. $y^2 = 8x$
9. $c = \sqrt{4+5} = 3$
10. $c = 3$; $e = 3/5 = 0.6$
11. $(x-2)^2+(y+5)^2 = 9$; center $(2,-5)$, $r=3$
12. Parabola
13. Circle
14. Greater than
15. $b = \sqrt{100-36} = 8$
16. $p = -4$; directrix $y = 4$
17. $r = \sqrt{9+16} = 5$; $(x-3)^2+(y+2)^2=25$
18. $(0, \pm 3)$
19. $2a = 18$
20. $9 - 4(2)(-2) = 25 > 0$ → Hyperbola