# Algebra Examples

, ,

There are two general equations for an ellipse.

Horizontal ellipse equation

Vertical ellipse equation

Use the distance formula to determine the distance between the two points.

Substitute the actual values of the points into the distance formula.

Simplify.

Multiply by .

Subtract from .

Remove parentheses around .

Raise to the power of .

Multiply by .

Subtract from .

Remove parentheses around .

Raising to any positive power yields .

Add and .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Use the distance formula to determine the distance between the two points.

Substitute the actual values of the points into the distance formula.

Simplify.

Multiply by .

Subtract from .

Remove parentheses around .

Raise to the power of .

Multiply by .

Subtract from .

Remove parentheses around .

Raising to any positive power yields .

Add and .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Rewrite the equation as .

Simplify each term.

Remove parentheses around .

Raise to the power of .

Raise to the power of .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Add and .

Multiply each term in by

Multiply each term in by .

Simplify .

Multiply by .

Multiply by .

Multiply by .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

is a distance, which means it should be a positive number.

Slope is equal to the change in over the change in , or rise over run.

The change in is equal to the difference in x-coordinates (also called run), and the change in is equal to the difference in y-coordinates (also called rise).

Substitute in the values of and into the equation to find the slope.

Simplify.

Simplify the numerator.

Multiply by .

Subtract from .

Simplify the denominator.

Multiply by .

Subtract from .

Divide by .

The general equation for a horizontal ellipse is .

Substitute the values , , , and into to get the ellipse equation .

Multiply by .

Simplify the denominator.

Remove parentheses around .

Raise to the power of .

Multiply by .

Simplify the denominator.

Remove parentheses around .

Rewrite as .