Question

Latus rectum of the parabola whose focus is $(3,4)$ and whose tangent at vertex has the equation $x+y=7+5\sqrt{2}$ is -

• A. $5$
• B. $10$
• C. $20$
• D. $15$

Answer 1

Answer: (C)

$20$

Length of latus rectum will be four times the distance of focus from tangent at vertex

Length of latus rectum is $4\times \frac{|3+4-7-5\sqrt{2}|}{\sqrt{1+1}}=20$