Exam 22: Analytic Geometry

Write the equation of the circle $x^{2}+y^{2}+2 x-6 y+6=0$ in standard form.

Find the vertex, focus, focal width, and equation of the axis for the parabola: $(x+2)^{2}=16(y-5)$

Write the equation, in general form, for the following parabola: vertex at $(3,-1), L=24$ , opens upwards

Write the equation, in general form, for the parabola: passes through $(1,2),(2,3)$ , and $(5,4)$ , axis horizontal

Write the equation of the parabola in general form with horizontal axis and vertex at the origin for a parabolic wall mirror that is $2 \mathrm{~m}$ tall and $0.1 \mathrm{~m}$ deep.

Write the equation in general form, of the line passing through the point $(2,-3)$ and with a y-intercept of 1 .

Find the slope of a line having an angle of inclination of $0.957 \mathrm{rad}$ .

Find the vertex, focus, focal width, and equation of the axis for the parabola: $(x-4)=2(y+1)^{2}$

Determine the points of intercepts of the line $3 x-y-6=0$ , and the hyperbola $3 x^{2}-4 y^{2}=12$ .