Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

Match the values in this hyperbola to those of the standard form. The variable represents the x-offset from the origin, represents the y-offset from origin, .

Find the distance from the center to a focus of the hyperbola by using the following formula.

Substitute the values of and in the formula.

Simplify.

Raise to the power of .

Rewrite as .

Use to rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Simplify the expression.

Add and .

Rewrite as .

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

The first focus of a hyperbola can be found by adding to .

Substitute the known values of , , and into the formula and simplify.

The second focus of a hyperbola can be found by subtracting from .

Substitute the known values of , , and into the formula and simplify.

The foci of a hyperbola follow the form of . Hyperbolas have two foci.

Find the Foci ((x+2)^2)/4-((y+1)^2)/5=1