Vertex of the equation is (-2, 5)
Focus of the equation is (-2, 8)
Directrix of the equation is 2
What is a Quadratic curve?
A quadratic curve is a parabolic curve is a graph of the points which define a quadratic function. It shows how a function behaves in the cartesian plane.
Quadratic curve may bend upwards, or downwards depending on the gradient of the curve.
Analysis:
setting the equation in the form, +4x -12y = -64 in the form = 4p(y-k)
Firstly we take -12y to the right hand side
+4x = 12y - 64
Making the left hand side a perfect square expression, we square both sides with -2
+4x + = 12y -64 +
= 12y -60
= 12(y - 5)
comparing with the other equation
-h = , h = -2, -k = - 5 k = 5, 4p = 12, p = 3
Vertex is (h, k) = (-2, 5)
Focus is (h, k+p) = (-2, 5+3) = (-2, 8)
Directrix is y = k-p = 5 - 3 = 2
Learn more about Quadratic curves: brainly.com/question/1214333
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