# Find the Directrix y^2+4x-14y=-53

Rewrite the equation in vertex form.
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.
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.
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 .
Move .
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.
Multiply by .
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 .
Raise to the power of .
Simplify the denominator.
Multiply by .
Combine and .
Divide by .
Move the negative one from the denominator of .
Rewrite as .
Multiply .
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
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.
Cancel the common factor of and .
Rewrite as .
Move the negative in front of the fraction.
Combine and .
Simplify the expression.
Divide by .
Divide by .
Multiply by .
Find the directrix.
The directrix of a parabola is the vertical line found by subtracting from the x-coordinate of the vertex if the parabola opens left or right.
Substitute the known values of and into the formula and simplify.
Find the Directrix y^2+4x-14y=-53