Q. Equation of the parabola with its vertex at $(1,1)$ and focus $(3,1)$ is
A) ${(x - 1)}^{2} = 8(y - 1)$
B) ${(y - 1)}^{2} = 8(x - 3)$
C) ${(y - 1)}^{2} = 8(x - 1)$
D) ${(x - 3)}^{2} = 8(y - 1)$
Explanation
(c)
Given vertex of parabola $(h,\ k) \equiv (1,\ 1)$
And its focus is $(a + h,\ k) \equiv (3,\ 1)$
Or $a + h = 3$
$\Rightarrow a = 2$
Since, $y$-coordinate of vertex and focus are same, therefore axis of parabola to $x$-axis. Thus, equation of parabola is
$(y - k)^{2} = 4a(x - h)$
$\Rightarrow \ {(y - 1)}^{2} = 8(x - 1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.