Q. The equation of latusrectum of a parabola is $x + y = 8$ and the equation of the tangent at the vertex is $x + y = 12,$ then length of the latusrectum is
A) $4\sqrt{2}$
B) $2\sqrt{2}$
C) 8
D) $8\sqrt{2}$
Explanation
(d)
Since, the equation of latusrectum and equation of tangent both are parallel and they lie in the same side of the origin
$\therefore a = \left| \frac{- 8 + 12}{\sqrt{1^{2} + 1^{2}}} \right| = \frac{4}{\sqrt{2}} = 2\sqrt{2}$
$\therefore$ Length of latusrectum $= 4a = 4\left( 2\sqrt{2} \right) = 8\sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.