Exam 22: Analytic Geometry

Find the coordinates of the center, vertices, and foci for the ellipse: $4 x^{2}+y^{2}-24 x-4 y+15=0$ . Use three significant digits if rounding is necessary.

Write the equation of the circle in general form with a radius $r=5$ if the line $x-2 y-1=0$ is a tangent to this circle at point $(3,1)$ .

Find the slope of the line having the given angle of inclination: $143^{\circ}$ . Use three significant digits.

Find the focus and focal width of this parabola: $x^{2}=12 y$

Write the equation of the hyperbola $\frac{(x+2)^{2}}{16}-\frac{(y-5)^{2}}{9}=1$ in general form.

Write the equation of the circle in general form: center at $(4,-7)$ , passes through $(1,-3)$

Find the angle of inclination, in radians, of a line having a slope of $m=-\frac{2}{3}$ .

Find the distance between the points $(-5.3,8.4)$ and $(9.2,-3.0)$ . Keep three significant digits.

Find the vertices, foci, and the slope of the asymptotes for the hyperbola: $25 x^{2}-81 y^{2}=2025$

Find the vertices, foci, and the slope of the asymptotes for the hyperbola: $9 y^{2}-25 x^{2}=225$

Write the equation of the hyperbola in general form: center at $(-2,-3)$ , horizontal transverse axis 24 units long, conjugate axis 12 units long

Determine the equation of the tangent to the circle: $x^{2}+y^{2}=169$ at $(12,5)$

Write the equation of the ellipse, whose center is at the origin, and passes through $(2,5)$ and $(6,-3)$ , in general form.

Write the equation of the circle $(x-4)^{2}+(y+3)^{2}=9$ in general form.

The angle of inclination of a set of stairs is $32.4^{\circ}$ . If the total rise of the stairs is $2.6 \mathrm{~m}$ , what is the total run of the stairs?

Find the angle of intersection between the line $y=\frac{3}{4} x-2$ and the line $y=-\frac{1}{3} x+1$ .

A loading ramp has a rise of $2.3 \mathrm{~m}$ and a run of $8.1 \mathrm{~m}$ , what is the angle of inclination of the ramp?

Determine the coordinates of the points of intercepts of the circle $(x-4)^{2}+(y+3)^{2}=25$ with the coordinate axes.

Find the center, vertices, foci, and the slope of the asymptotes for the hyperbola: $51 y^{2}-49 x^{2}-204 y$ $-98 x-2344=0$

Find the angle of inclination, in decimal degrees, of a line passing through the points $(8,-3)$ and $(5,6)$ .