Conic Sections Question 37
Question: Equation of the parabola with its vertex at (1, 1) and focus (3, 1) is
[Karnataka CET 2001, 02]
Options:
A) $ {{(x-1)}^{2}}=8(y-1) $
B) $ {{(y-1)}^{2}}=8(x-3) $
C) $ {{(y-1)}^{2}}=8(x-1) $
D) $ {{(x-3)}^{2}}=8(y-1) $
Show Answer
Answer:
Correct Answer: C
Solution:
Given, vertex of parabola (h, k) $ \equiv $ (1, 1) and its focus $ (a+h,k)\equiv (3,1) $ or $ a+h=3 $ or $ a=2. $
We know that as the y-coordinates of vertex and focus are same, therefore axis of parabola is parallel to x-axis.
Thus equation of the parabola is $ {{(y-k)}^{2}}=4a(x-h) $ or $ {{(y-1)}^{2}} $
$ =4\times 2(x-1) $ or $ {{(y-1)}^{2}}=8(x-1). $
BETA
