Question

If the focus of a parabola is $(-2,1)$ and equation of the directrix is $x+y=3$, find the vertex of the parabola.

Answer 1

$x+y=3m=-1$

$(-2,1)m=1$

$y-1=1(x+2)$

$y-1=x+2$

$x-y+3=0$

$x-y+3=0$

$x+y-3=0$

$2x=0$

$x=0;y=3$

Vertex=

Midpoint of focus and directrix

$=\frac{0-2}{2},\frac{3+1}{2}=(-1,2)$