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

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

${\left(y - 1\right)}^{2} = - 12 \left(x + 2\right)$

#### Explanation:

In general, the equation of parabola with the vertices $\left({x}_{1} , {y}_{1}\right)$ & directrix $x = k \setminus \left(\setminus \forall a > 0\right)$ is a horizontal parabola diverging in -ve x-direction & is given as follows

${\left(y - {y}_{1}\right)}^{2} = - 4 \left(k - {x}_{1}\right) \left(x - {x}_{1}\right)$

Hence the equation of parabola with the vertices $\left({x}_{1} , {y}_{1}\right) \setminus \equiv \left(- 2 , 1\right)$ & directrix $x = 1$ is given by setting ${x}_{1} = - 2 , {y}_{1} = 1$ & $k = 1$ in above general formula as follows

${\left(y - 1\right)}^{2} = - 4 \left(1 - \left(- 2\right)\right) \left(x - \left(- 2\right)\right)$

${\left(y - 1\right)}^{2} = - 12 \left(x + 2\right)$