Conic Sections Question 44
Question: If (0, 6) and (0, 3) are respectively the vertex and focus of a parabola, then its equation is
[Karnataka CET 2004]
Options:
A) $ x^{2}+12y=72 $
B) $ x^{2}-12y=72 $
C) $ y^{2}-12x=72 $
D) $ y^{2}+12x=72 $
Show Answer
Answer:
Correct Answer: A
Solution:
Here vertex $ \equiv $ (0, 6) and focus $ \equiv $ (0, 3) then $ Z\equiv (0,9) $ i.e., $ y=9 $
$ \therefore $ Equation of parabola, $ SP=PM $
$ \Rightarrow $ $ \sqrt{{{(x-0)}^{2}}+{{(y-3)}^{2}}}=|y-9| $
$ \Rightarrow $ $ x^{2}+y^{2}-6y+9=y^{2}-18y+81 $
or $ x^{2}+12y=72 $ .
BETA
