Pre-Calculus
Introduction to Conic Sections
Conic Sections
 A Circle is formed if the plane is parallel to the
base of the cone.
 A Parabola is fromed if the plane is parallel to
the slanting height of the cone.
 An Ellpise is formed when the (tilted) plane
intersects only one cone to form a bounded curve.
 A hyperbola is formed when the plane (not
necessarily vertical) intersects both cones to form
an unbounding curves
Parts of a Cone
Circle
 Is the set of all points in a plane that are at a
constant distance, the radius from the fixed point.
The fixed point is called the center of the cricle.
Standard Form
( x - h )^2 + ( y - k )^2 = r^2
Center = ( h, k )
General Form
x^2 + y^2 + Dx + Ey + F = 0
center =
( - D/2 , -E/2 )
All the points in the cricle are equidistant to the
center, the radius is half the diameter. And twice the
size of the radius is the size of the diameter.
Now what we need to know first is how you can transfrom
general form to standard form. For example:
Transfrom the General Form
x^2 + y^2 – 10x + 4y – 7 = 0 of a circle into a
standard form. Find the center and the radius.
 We can transform by using “completing the square”
So what does “completing the square” mean? It means
getting your equation to neat perfect square form.