Question

The equation of the parabola whose focus (3, 2) and vertex (1, 2), is

• A. $ {{x}^{2}}+4x-8y+12=0 $
• B. $ {{x}^{2}}-4x-8y+12=0 $
• C. $ {{y}^{2}}-8x-4y+12=0 $
• D. $ {{y}^{2}}+4y-8x+12=0 $
• E. $ {{y}^{2}}-8x-2y-17=0 $

Answer 1

Answer: (C)

Given, F(3, 2) and V(1, 2). Here, we see that y-coordinates are same, it means that axis of the parabola is parallel to $ x- $ axis. Here, $ a=3-1=2 $
$ \therefore $ Required equation of parabola is
$ {{(y-2)}^{2}}=4\times 2(x-1) $
$ \Rightarrow $ $ {{y}^{2}}-4y-8x+12=0 $