Question

The equation of latus rectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x+y = 12, then length of the latus rectum is

• A.
  
• B.
  
• C. 8
• D.

Answer 1

The correct option is D

Clearly; $a=\left|\frac{-8}{\sqrt{1+1}}\right|-\left|\frac{-12}{\sqrt{1+1}}\right|=\frac{4}{\sqrt{2}}$
Length of latus rectum $=4a=4\times \frac{4}{\sqrt{2}}=8\sqrt{2}$.