Exam 22: Analytic Geometry

Find the center and radius of the circle: $(x-8)^{2}+(y+5)^{2}=121$

Find the coordinates of the center, vertices, and foci for the following ellipse: $2 x^{2}+y^{2}-20 x+14 y+$ $79=0$

Write the equation of a parabola with vertex at the origin that passes through $(2,3)$ and has a vertical axis.

Find the distance between the points $(-35,81)$ and $(66,21)$ . Keep three significant digits.

Find the coordinates of vertices and foci for the equation. Use three significant digits if rounding is necessary.

Using a ladder to reach the top of a $12-\mathrm{m}$ tall building, the ladder must not exceed an angle of $65^{\circ}$ with the ground to be safe. How far from the base of the building must the foot of the ladder be in order to be safe?

Find the coordinates of the vertices and foci for this ellipse: $2 x^{2}+9 y^{2}=18$ . Use three significant digits if rounding is necessary.

Find the vertex, focus, the focal width, and the equation of the axis for the parabola: $(x-3)^{2}=5(y+2)$

Write the equation, in general form, of the line passing through the points $(-4,2)$ and $(6,-6)$ .

Solve simultaneously to find the points of intersection (if any) of the ellipse with the given curve: $x^{2}+$ $4 y^{2}=40$ with $3 x+2 y-20=0$

Find the slope of the line passing through the points $(-5,-7)$ and $(3,-1)$ .

Find the center and radius of the circle: $x^{2}+y^{2}+10 x-4 y=52$

Find the angle of inclination, in decimal degrees, of a line having a slope of $m=-5.5$ .

The highway regulations in a certain state say an interstate cannot rise more than $6.0 \mathrm{~m}$ for every $1 \overline{0} 0 \mathrm{~m}$ the road extends horizontally. What is the maximum angle of inclination a highway in this state can have?

Find the vertex, focus, the focal width, and the equation of the axis for the parabola: $y^{2}+4 x-6 y+$ $17=0$

Find the focus and focal width of this parabola: $4 y^{2}+7 x=0$

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 $y$ -axis.

Write the equation, in slope-intercept form, of the line that passes through the point $(5,4)$ and perpendicular to the line $5 x-2 y-10=0$ .

Find the angle of intersection between the line $y=4 x+5$ and the line $2 y-x=8$ . Use three significant digits.

Find the angle of inclination, in decimal degrees, of a line passing through the points $(-5.2,5.4)$ and $(4.3,-3.5)$ .