# 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 to get .

Subtract from to get .

Raise to the power of to get .

Multiply by to get .

Subtract from to get .

Remove parentheses around .

Raising to any positive power yields .

Add and to get .

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 to get .

Subtract from to get .

Raise to the power of to get .

Multiply by to get .

Subtract from to get .

Remove parentheses around .

Raising to any positive power yields .

Add and to get .

Any root of is .

Move to the right side of the equation by subtracting from both sides of the equation.

Multiply each term in by

Multiply each term in by .

Simplify .

Multiply by to get .

Multiply by to get .

Multiply by to get .

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

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

Simplify the right side of the equation.

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

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 to get .

Subtract from to get .

Simplify the denominator.

Remove parentheses.

Multiply by to get .

Subtract from to get .

Divide by to get .

The general equation for a horizontal ellipse is .

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

Multiply by to get .

Split the fraction into multiple fractions.

Remove parentheses around .

Raise to the power of to get .

Multiply by to get .

Split the fraction into multiple fractions.

Apply the product rule to .

Raise to the power of to get .

Rewrite as .

Multiply by to get .