Parabolas Page 8

Page 8

Rewriting the Equation of a Parabola from
Standard Form to General Form

In the previous modules, you were able to obtain the general equation of an ellipse and a circle by expanding their standard forms.

You can also obtain the general equation of a parabola by expanding its standard form.

Let's look at a few examples to see how you can rewrite the standard equation of a pararbola into the form Ax² + By² + Cx + Dy + F = 0

EXAMPLE 1:

The parabola shown here is described by the equation y + 2 = (1/2)(x - 3)².

Write this equation in the form Ax² + By² + Cx + Dy + F = 0.

Equation to expand y + 2 = (1/2)(x-3)²

Multiply by 2 to clear all fractions 2y + 4 = (x - 3)²

Expand the squared terms 2y + 4 = x² - 6x + 9

Simplify x² - 6x - 2y + 5 = 0

EXAMPLE 2

The parabola on the left is described by the equation x = (1/100)y².

Write this equation in the form Ax² + By² + Cx + Dy + F = 0.
Equation to expand x = (1/100)y²

Multiply by 100 to clear all fractions 100x = y²

Simplify y² - 100x = 0

EXAMPLE 1:
The parabola shown here is described by the equation y + 2 = (1/2)(x - 3)².
	Write this equation in the form Ax² + By² + Cx + Dy + F = 0.
	Equation to expand	y + 2 = (1/2)(x-3)²
	Multiply by 2 to clear all fractions	2y + 4 = (x - 3)²
	Expand the squared terms	2y + 4 = x² - 6x + 9
	Simplify	x² - 6x - 2y + 5 = 0

EXAMPLE 2
	The parabola on the left is described by the equation x = (1/100)y².
	Write this equation in the form Ax² + By² + Cx + Dy + F = 0.
	Equation to expand	x = (1/100)y²
	Multiply by 100 to clear all fractions	100x = y²
	Simplify	y² - 100x = 0