Question

Let two tangents $3x-4y+20=0$ and $x-y-3=0$ of a parabola intersect the tangent at vertex at points $P\left(0 , 5\right)$ and $Q\left(3 , 0\right)$ respectively, then the length of latus rectum is

• A. $\frac{12}{\sqrt{34}}$
• B. $\frac{18}{\sqrt{34}}$
• C. $\frac{24}{\sqrt{34}}$
• D. $\sqrt{34}$

Answer 1

Answer: (C)

Focus is $\left(6 , - 3\right)$ and equation of tangent at vertex is $5x+3y-15=0$
$\therefore LR=4\left|\frac{30 - 9 - 15}{\sqrt{34}}\right|=\frac{24}{\sqrt{34}}$