Question

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

• A. $x^2-6x+24y-63=0$
• B. $x^2-6x+24y+81=0$
• C. $y^2-6y+24x-63=0$
• D. $y^2-6y-24x+81=0$

Answer 1

Answer: (C)

$y^2-6y+24x-63=0$

Given vertex and focus of a parabola are $(3,3)$ and $(-3,3)$.

So, $y=3$ is axis of parabola.

Now, the general equation of this parabola is given by

${(y-3)}^2=-4a(x-3)$

And we know that distance between vertex and focus is equal to $a=6$

$\Rightarrow y^2-6y+24x-63=0$