Questions in Section Algebra II

Use the distance formula to write the equation of the parabola with the focus `F=(0,-1)` and the directrix `y=1`.

The fourth roots of `1296i`.

Find the vertex, focus, and directrix of the parabola `(x-2)^2=-(y+1)`. Graph the equation.

Analyze the equation. That is, find the center, vertices, and foci of the ellipse `16x^2+y^2=576` and graph it.

Prove that `tan^2(x)-sin^2(x)=tan^2(x)sin^2(x)`.

A parabola can be drawn given a focus of `(7,-8)` and a directrix of `y= -6`. What can be said about the parabola?

Find equation of the line parallel to the line `y=-4x+3/2 ` passing htrough the point `(7,-1)`.

Write an equation of the parabola in vertex form that passes through `(-7,-15)` and has vertex `(-5,9)`.

If `r(x) = 1+3x` , find `r(x+2)`.

Find the foci, eccentricity and the directrices of the given ellipse `2x^2+ y^2-4y+3=0`.