Find an equation of the parabola with vertex, - 5 - 5 and directrix = x - 12.

x=-y26+y3-136

Explanation:

Given -

Vertex (-2,1)

Directrix x=1

The vertex is in the 2nd quadrant. The directrix is parallel to the y-axis. So, the parabola opens to the left. The vertex of the parabola is not the origin. Then its general form is -

(y-k) 2=-4. a. (x-h)

Where -

h and k are the coordinates of the vertex.

h=-2)

k=1

a=1.5 half the distance between Directrix and vertex [ = distance between focus and vertex]

Substitute these values in the equation

(y-1) 2=-4.1.5. (x+2)

y2-2y+1=-6x-12

-6x-12=y2-2y+1

-6x=y2-2y+1+12

x=y2-6-2y-6+13-6

x=-y26+y3-136