# Find the Focus (y-3)^2=12(x-1)

Rewrite the equation in vertex form.
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 .
Add to 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 .
Subtract from .
Apply the distributive property.
Simplify.
Combine and .
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Simplify the expression.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
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 the numerator by the reciprocal of the denominator.
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.
Simplify.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Find the value of using the formula .
Simplify each term.
Simplify the numerator.
Apply the product rule to .
Raise to the power of .
Apply the product rule to .
One to any power is one.
Raise to the power of .
Combine and .
Multiply by .
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.
Combine and .
Combine the numerators over the common denominator.
Subtract from .
Divide 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 the focus.
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.
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 .
Find the focus.
The focus of a parabola can be found by adding to the x-coordinate if the parabola opens left or right.
Substitute the known values of , , and into the formula and simplify.
Find the Focus (y-3)^2=12(x-1)