Writing assignment 3 - Writing assignment#3 Scott B Roberts...

Writing assignment #3
Scott B. Roberts
Math 151
There are three different types of conic sections that we examined in class. They include
the parabola, ellipse, and the hyperbola. Conics are curves that are formed by
intersecting a cone with a plane. The conic section we end up with is dependant upon the
degree that the plane intersects the cone.
All of the conic sections we saw in class are derived from the same general quadratic
equation: Ax 2 + Bxy + Cy 2 + Dx + Ey + F=0
The determinant of the equation is B
2
- 4 AC . Assuming a conic is not degenerate, the
following conditions hold true: If B
2
-4 AC > 0, the conic is a hyperbola. If B
2
-4 AC < 0, the
conic is a circle, or an ellipse. If B
2
- 4 AC = 0, the conic is a parabola
A parabola is the set of all points (x,y) that are the same distance from a fixed line (called
the directrix) and a fixed point (called the focus). It takes the shape that is similar to the
letter U.
Parabola== ( y − k)
2
= 4 p ( x − h )
2
is the equation with axis parallel to the x-axis, or
( x − h) 2 = 4 p ( y − k )