AP®︎ Precalculus: Topic 4.6 Practice Test

Essential Knowledge: 4.6.A.1

A parabola with vertex $(h, k)$ can, if $a \ne 0$, be represented analytically as $x - h = a(y - k)^2$ if it opens left or right, or as $y - k = a(x - h)^2$ if it opens up or down.

Essential Knowledge: 4.6.A.2

An ellipse centered at $(h, k)$ with horizontal radius $a$ and vertical radius $b$ can be represented analytically as $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$. A circle is a special case of an ellipse where $a = b$.

Essential Knowledge: 4.6.A.3

A hyperbola centered at $(h, k)$ with vertical and horizonal lines of symmetry can be represented algebraically as $\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$ for a hyperbola opening left and right, or as $\frac{(y - k)^2}{b^2} - \frac{(x - h)^2}{a^2} = 1$ for a hyperbola opening up and down. The asymptotes are $y - k = \pm \frac{b}{a}(x - h)$.