09 Conic Sections Online Quiz Questions

Which distance property defines a parabola?

For the ellipse $\frac{(x-1)^2}{25}+\frac{(y+2)^2}{9}=1$, which pair gives the vertices?

For $\frac{(x+3)^2}{16}-\frac{(y-1)^2}{9}=1$, which statement correctly identifies the hyperbola's orientation and vertices?

Select all statements that correctly describe the standard forms or orientation of parabolas.

Select all statements that correctly describe ellipses.

True or false: In a nonrotated conic, opposite signs on the $x^2$ and $y^2$ terms indicate a hyperbola.

True or false: For a hyperbola, the focal relationship is $c^2=a^2-b^2$.

For the parabola $(x-2)^2=8(y+1)$, what is the value of $p$?

After completing the square, $y^2-6y-4x+1=0$ becomes $(y-3)^2=4(x+2)$. What is the vertex of this parabola? Enter the vertex as a LaTeX-delimited ordered pair.

Analyze the ellipse $\frac{(x-1)^2}{25}+\frac{(y+2)^2}{9}=1$. Identify its center, major-axis direction, vertices, co-vertices, and foci, showing how you determine the focal distance.

Classify the nonrotated equation $4x^2+4y^2-8x+16y-11=0$ by examining its squared terms.

A general quadratic equation contains an $xy$ term. What type of conic orientation may this indicate?

Classify the nonrotated conic represented by $9x^2+4y^2-18x+16y-11=0$.

True or false: If a nonrotated conic has equal positive coefficients on $x^2$ and $y^2$, it is a circle.

For the parabola $(x-2)^2=8(y+1)$, which point is the focus?

For the parabola $(y+3)^2=-12(x-1)$, enter the value of $p$.

Which pair gives the vertices of the ellipse $\frac{(x-1)^2}{25}+\frac{(y+2)^2}{9}=1$?

Which pair gives the asymptotes of the hyperbola $\frac{(y-2)^2}{16}-\frac{(x+1)^2}{9}=1$?