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 $(h,k) = (1,1)$ and its focus $(a + h,k) = (3,1)$ or $a + h = 3$
$\Rightarrow \ \ a = 2$
Since, $y$-coordinate of vertex and focus are same, therefore axis of parabola is parallel 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.