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,\text{ }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) $