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

step-by-step explanation: