Find the standard form of the equation of the parabola with the given characteristics?

Vertex: (-2, 1)
Directrix: x = 1

1 Answer

#(y-1)^2=-12(x+2)#

Explanation:

In general, the equation of parabola with the vertices #(x_1, y_1)# & directrix #x=k \ (\forall a>0)# is a horizontal parabola diverging in -ve x-direction & is given as follows

#(y-y_1)^2=-4(k-x_1)(x-x_1)#

Hence the equation of parabola with the vertices #(x_1, y_1)\equiv(-2, 1)# & directrix #x=1# is given by setting #x_1=-2, y_1=1# & #k=1# in above general formula as follows

#(y-1)^2=-4(1-(-2))(x-(-2))#

#(y-1)^2=-12(x+2)#