SOLUTION: The vertex,focus and directrix of the parabola y^2+4x-16y+8=0

Question 972479: The vertex,focus and directrix of the parabola y^2+4x-16y+8=0
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
A reference model for a horizontal parabola is and allowing for translations of location, . These forms come from the derivation for the equation of a parabola. The meaning of p is the distance between the vertex (for standard position) and either the focus or the directrix.

Start from the general given equation, complete the square, and put into STANDARD FORM.

, the constant, 64 needed for completing the square for y.

-------still not exactly standard form, but vertex is (14,8), then corresponding coefficients gives and then .
The vertex occurs as a maximum for x value so the parabola opens to the left, and therefore the focus is 1 unit to the left of the vertex.
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Focus is (13,8);
Directrix is x=15.
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