Question

The equation of the parabola whose focus is $(4,-3)$ and vertex is $(4,-1)$

• A. $x^2-8x+8y+24=0$
• B. $x^2-8x-8y+8=0$
• C. $x^2-8x+8y+8=0$
• D. $x^2-8x+8y+32=0$

Answer 1

The correct option is A $x^2-8x+8y+24=0$

$\because x$ coordinates of the vertex and the focus both are same
$\therefore$ axis of the required parabola will be $x=4$
If we shift the origin at $(4,-1)$, then the parabola will be the form of $X^2=-4aY$
and $a=\text{distance between focus and vertex}=2$
So required parabola will be
$(x-4{)}^2=-8(y+1)$
$\Rightarrow x^2-8x+8y+24=0$