Question

Find the vertex, focus and diretrix of x^2+4x-12y=-64
It needs to be in (x-h)^2=4p(y-k) form

Answer 1

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, $x^{2}$ +4x -12y = -64 in the form $(x-h)^{2}$ = 4p(y-k)

Firstly we take -12y to the right hand side

$x^{2}$ +4x = 12y - 64

Making the left hand side a perfect square expression, we square both sides with -2

$x^{2}$ +4x + $(2)^{2}$ = 12y -64 + $(2)^{2}$

$(x+2)^{2}$ = 12y -60

$(x+2)^{2}$  = 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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