Hard Conic Sections Quiz with Answers (Parabola–Hyperbola)

Question 1

Identify the conic and its orientation:

$$9x^2-16y^2=144$$

Accepted Answer

Hyperbola, opens left/right

Answer

Hyperbola, opens up/down

Answer

Parabola, opens left/right

Answer

Ellipse, major axis horizontal

Question 2

Identify the conic (after simplification):

$$x^2-6x+y^2+10y+9=0$$

Accepted Answer

Circle

Answer

Parabola

Answer

Ellipse

Answer

Hyperbola

Question 3

A conic has eccentricity $e=\frac{3}{2}$ and a directrix $x=-2$, with the conic opening to the right. Which equation matches this information?

Accepted Answer

$\frac{(x-1)^2}{1}-\frac{y^2}{\frac{5}{4}}=1$

Answer

$\frac{(x+2)^2}{9}+\frac{y^2}{4}=1$

Answer

$(y)^2=6(x+2)$

Answer

$\frac{(y)^2}{1}-\frac{(x+2)^2}{\frac{5}{4}}=1$

Trusted & Recognized