Exam 22: Analytic Geometry

Write the equation, in slope-intercept form, of the following line: passes through $(-2,-1)$ ; parallel to $y=-1 / 2 x+3$

Find the center and radius of the circle: $x^{2}+y^{2}=64$

Find the distance between the given points: $(0,5)$ and $(1,-4)$

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

A certain house has a roof with a $7 / 12$ pitch. In other words, the roof goes up 7 inches for every 12 inches across. What is the angle of inclination for the roof, to three significant digits?

Solve simultaneously to find the points of intersection (if any) of the ellipse with the given curve: $25 x^{2}+9 y^{2}=900 \text { with } x^{2}=8 y$

Find the distance between the points $(b+2,5)$ and $(b-3,-2)$ . Keep three significant digits.

Find the angle of inclination, in decimal degrees, of a line having the given slope: $m=-3.10$

Find the angle of intersection between line 1 having an angle of inclination of $78^{\circ}$ and line 2 having an angle of inclination of $145^{\circ}$ .

Find the directed distance $A B$ if $A=(9,-1)$ and $B=(3,-1)$ .

Find the point(s) of intersection: $x^{2}+y^{2}+2 x-2 y-23=0$ and $x^{2}+y^{2}-6 x+12 y-35=0$

Write the equation, in general form, for the following parabola: vertex at $(2,-5), L=16$ , opens to the right

Write the equation of the tangent to the circle at the given point: $(x-3)^{2}+(y+5)^{2}=25$ at $(0,-1)$

Solve simultaneously to find the points of intersection (if any) of the ellipse with the given curve: $9 x^{2}+$ $16 y^{2}=144$ with $2 x-y-3=0$

Write the equation, in slope-intercept form, of the line that passes through the point $(-4,7)$ and perpendicular to the line $4 x-3 y+2=0$ .

Find the slope of a line perpendicular to a line having a slope of $m=-4.80$ .

Find the point(s) of intersection: $x^{2}+y^{2}-14 y-51=0$ and $x^{2}+y^{2}+20 x-36 y+399=0$

Determine the value of $a$ , so that the line $(a+2) x+\left(a^{2}-a\right) y+3 a^{2}-8 a+5=0$ is parallel to the $x$ -axis.

Write the equation in general form of the ellipse $\frac{(x-2)^{2}}{16}+(y+3)^{2}=1$ .

Find the slope of a line perpendicular to a line having an angle of inclination of $15 \overline{0}^{\circ}$ .