### Compute the center of the curve

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ANALYTIC GEOMETRY (STRAIGHT LINES & CONICS)

Straight Lines
A line has an equation of x + 5y + 5 = 0.

1. Find the equation of the line through point (3,1) that is perpendicular to this line.
2. Find the equation of the line through point (3,1) that is parallel to this line.

Parabola
A parabola has an equation of y5 = Cx - D. The distance of the latus rectum is 4. If the distance of the axis of the parabola to x-axis is zero.
1. Compute the value of C.
2. Compute the value of D.
3. Compute the equation of the directrix

Ellipse

An ellipse has an equation equal to 9x2 - 144x + 16y2 + 96y + 576 = 0.
1. Compute the center of the curve.
2. Compute the eccentricity of the curve.
3. Compute the length of the latus rectum.

Some questions for general equations of conics:

What conic section is represented by x2 - 4y2 + 8x + 4y = 15?

The equation x2 + y2 - 4x + 2y - 20 = 0 describes:
a. Circle
b. Ellipse
c. Parabola
d. Hyperbola

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