Isolate to the left side of the equation.

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

Subtract from both sides of the equation.

Add to both sides of the equation.

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Move the negative in front of the fraction.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Complete the square for .

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.

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.

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 .

One to any power is one.

Raise to the power of .

Simplify the denominator.

Multiply by .

Combine and .

Reduce the expression by cancelling the common factors.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Move the negative in front of the fraction.

Multiply .

Multiply by .

Multiply by .

Combine the numerators over the common denominator.

Add and .

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 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 focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.

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

Find the Focus x^2-2x+16y-47=0