Question

Find the equation of the parabola with

(a) Focus at $F\left(-1,-3\right)$ and the line $y=1$ as the directrix.

Answer 1

REF .Image

V is the vector of

parabola which

will he the midpoint

of (-1,1) and (-1,3)

$\therefore V(-1,-1)(h,k)$

So, equation of parabola will be

$(x+1{)}^2=-4a(y+1)$

where a = distance between vertex and focus

$\therefore a=2$

$\therefore$ equation of parabola $\Rightarrow (x+1{)}^2=-8(y+1)$