Find the Directrix y^2-5x+12y=-16

Math
Rewrite the equation in vertex form.
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Isolate to the left side of the equation.
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Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify each term.
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Dividing two negative values results in a positive value.
Dividing two negative values results in a positive value.
Dividing two negative values results in a positive value.
Complete the square for .
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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.
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Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
Find the value of using the formula .
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Simplify each term.
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Simplify the numerator.
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Apply the product rule to .
Raise to the power of .
Raise to the power of .
Combine and .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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.
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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.
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Combine and .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Find the directrix.
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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^2-5x+12y=-16

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