Isolate to the left side of the equation.

Rewrite the equation as .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Subtract from both sides of the equation.

Reorder terms.

Complete the square for .

Simplify each term.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Multiply by .

Add and .

Apply the distributive property.

Simplify.

Combine and .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Combine and .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Simplify each term.

Move the negative in front of the fraction.

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Use the form , to find the values of , , and .

Consider the vertex form of a parabola.

Substitute the values of and into the formula .

Simplify the right side.

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Divide by .

Find the value of using the formula .

Subtract from .

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raising to any positive power yields .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by zero.

Divide by .

Multiply by .

Substitute the values of , , and into the vertex form .

Set equal to the new right side.

Use the vertex form, , to determine the values of , , and .

Find the vertex .

Find the distance from the vertex to a focus of the parabola by using the following formula.

Substitute the value of into the formula.

Simplify.

Cancel the common factor of and .

Rewrite as .

Move the negative in front of the fraction.

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply by .

The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.

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

Find the Directrix (x+4)^2=-36(y+6)