Exam 22: Analytic Geometry

Find the center and radius of the circle: $x^{2}+y^{2}-18 y=-17$

Write the equation of the ellipse, whose center is at the origin, and passes through $(0,4)$ and $(1,2 \sqrt{3})$ , in general form.

Write the equation, in general form, of the line: $y$ -intercept $=12$ and parallel to $4 x+5 y=8$

Write the equation of the circle in standard form: center at $(2,5)$ , radius $=3$

Determine the equation of the tangents to the circle: $x^{2}-40 x+y^{2}=0$ at $(32,16)$

Determine the coordinates of the points of intercepts of the circle $(x-5)^{2}+(y-12)^{2}=169$ with the coordinate axes.

Determine the points of intersection of the line $x+2 y-1=0$ , and the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$ .

Find the slope of a line perpendicular to a line having an angle of inclination of $4.85 \mathrm{rad}$ .

Write the equation of a hyperbola with center at the origin, vertex at $(-8,8)$ , and asymptotes on the coordinate axes.

Write the equation of the ellipse: center at $(9,-5)$ , vertex at $(-1,-5)$ and focus at $(12,-5)$

Find the focus and focal width of this parabola: $y^{2}=10 x$

Find the coordinates of vertices and foci for the ellipse: $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ . Use three significant digits if rounding is necessary.

Write the equation, in slope-intercept form, of the line passing through the points $(-2,1)$ and $(3,-4)$ .

Find the slope of a line having an angle of inclination of $0.625 \mathrm{rad}$ .

Find the angle of inclination, in decimal degrees, of a line having a slope of $m=10$ .

Find the slope of the line passing through the points $(3, b-2)$ and $(5-b, 4)$ .

Find the directed distance $A B$ if $A=(5,-4)$ and $B=(7,-4)$ .

Write the equation, in general form, of the line in the graph below:

Write the equation, in general form, for the following parabola: vertex at $(0,1), L=20$ , opens upwards

Determine the value of $a$ , so that the line $(a+2) x+\left(a^{2}-a\right) y+4 a^{2}+3 a-7=0$ passes through the origin.