Exam 1: Analytic Geometry

For the problems below, find the vertices, foci, and lengths of the transverse and conjugate axis for each hyperbola. Find the equations of the asymptotes. -Find the equation of the hyperbola with foci at $(0, \pm 7)$ and transverse axis of length 10.

Find the center and radius of the given circle. $x^{2}+y^{2}-6 x+4 y-3=0$ .

Find the equation of the line that passes through $(-5,13)$ with slope -0.75.

Graph each equation. - $y=x^{3}-5 x^{2}+12$

Find the coordinates of the point midway between (4, - 6) and (-9, 14).

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. -Find the equation of the ellipse with vertices at $(0, \pm 8)$ , and with a minor axis of length 10 .

For the point $\left(4,45^{\circ}\right)$ , name three other sets of polar coordinates such that - $360^{\circ} \leq \theta \leq 360^{\circ}$ .

Find the $x$ - coordinates(s) of the solution(s) to the system of equations: $\mathrm{x}^{2}+\mathrm{y}^{2}-4 \mathrm{x}-21=0$ and $\mathrm{y}=2 \mathrm{x}-3$ .

Find the equation of a line that passes through $(-12,6)$ and is perpendicular to $4 x-3 y=8$ .

Change $x^{2}+y^{2}=49$ to polar form.

Change $x^{2}+y^{2}-4 x-12 y=0$ into an equation in polar form.

For the problems below, find the vertices, foci, and lengths of the major and minor axis of each ellipse. -Find the equation of the ellipse with vertices at $( \pm 7,0)$ and foci at $( \pm 2 \sqrt{10}, 0)$ .

Find the equation of the circle (in standard form) with center at ( $4,-1$ ) and radius 3.

Determine whether or not each relation is a function. Write its domain and range. -Given $f(x)=\frac{3 x-x^{2}}{x}$ , find a) $f(2)$ b) $\mathrm{f}(-4)$ c) $\mathrm{f}(3 \mathrm{a})$

Find the equation of a line that is perpendicular to the $x$ - axis and passes through the point $(5,-3)$ .

$r=7 \sin \theta$

Find the equation of a line that passes through $(8,-2)$ and is perpendicular to $3 x-5 y=16$ .

Find the equation of the ellipse with vertices of $(0,-18)$ and $(0,18)$ and minor axis of length 30.

Change $\left(5,60^{\circ}\right)$ to rectangular coordinates.

Determine whether the given pair of equations represents lines which are parallel, perpendicular, or neither. $2 x-3 y-3=0$ and $3 x+2 y-8=0$