Answer:
x=−y26+y3−136
Step-by-step 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