Question

If vertex and focus of a parabola are (3, 3) and $(-3,3),$ then its equation is

• A. ${(y+3)}^2$ $=24(x+3)$
• B. ${(y+3)}^2=-24(x+3)$
• C. ${(y-3)}^2=-24(x-3)$
• D. ${(y-3)}^2=24(x-3)$

Answer 1

Answer: (C)

Given, vertex $(h,k]=(3,3)$ and focus $(a+h,k)=(-3,3)$
$\Rightarrow$ $a+h=-3$
$\Rightarrow$ $a=-3-h$
$\Rightarrow$ $=-3-3=-6$
We know that, if y-coordinate of vertex and focus is same, then axis of parabola will be parallel to
$x-$ axis.
$\therefore$ ${(y-k)}^2=4a(x-h)$
$\Rightarrow$ ${(y-3)}^2=4(-6)(x-3)$
$\Rightarrow$ ${(y-3)}^2=24(x-3)$