Question

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

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

Answer 1

`(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)`