Exam 22: Analytic Geometry

Find the $x$ and $y$ intercepts for the circle: $x^{2}+y^{2}-6 x+8 y-11=0$ . Use three significant digits.

Write the equation, in slope-intercept form, of the following line: $y$ -intercept $=-a$ ; slope $=2 b$

Write the equation of the tangent to the circle at the given point: $(x-3)^{2}+(y+2)^{2}=100$ at $(-3,6)$

Write the equation of the following hyperbola in general form: foci at $(0, \pm 12)$ , transverse axis is 20 units long

Find the slope of the line having the given angle of inclination: $21.8^{\circ}$

Find the angle of inclination, in decimal degrees, of a line having a slope of $m=\frac{4}{7}$

Find the directed distance $B A: A(10.55,4.35), B(-5.55,4.35)$

Write the equation, in slope-intercept form, of line 1 in the graph below:

Write the equation of the hyperbola $4 x^{2}-25 y^{2}-24 x-50 y-89=0$ in standard form.

Write the equation neglecting air resistance, of the parabola in general form, that describes the trajectory of a baseball that reaches a maximum height of $25 \mathrm{~m}$ and travels a distance of $60 \mathrm{~m}$ .

Write the equation of the parabola in general form of a parabolic archway between 2 rooms that is 3.5 $\mathrm{m}$ tall and $8 \mathrm{~m}$ wide. The parabola should pass through the origin.

Write the equation, in general form, of the line: slope $=1 / 4, y$ -intercept $=-3$

Write the equation, in general form, for the following parabola: vertex at $(-3,5), L=8$ , opens to the left

Find the coordinates of the center, vertices, and foci for the following ellipse: $\frac{(x+1)^{2}}{64}+\frac{(y-5)^{2}}{100}=1$

Find the slope and $y$ -intercept for the equation $y=-2$ .

Write the equation of the ellipse centered at the origin, with vertical major axis 10 units long and a focus at $(0,3)$ .

Find the slope and $y$ -intercept for the equation $y=x+29$ .

Find the distance between the points $(101,2)$ and $(807,-3)$ . Keep three significant digits.

Write the equation in standard form of the ellipse with a vertical major axis 16 units long and horizontal minor axis is 6 units long and has a center (5, -4).

Write the equation, in slope-intercept form, of the following line: passes through (-2.31, 4.05); angle of inclination $=135^{\circ}$