Question

The equation of latus rectum of parabola is $x + y = 8$ and the equation of the tangent of the vertex is $x +y = 12$ and length of the latus rectum is $a\sqrt{2}$ , then the value of a is

Answer 1

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