Question

If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x + y = a, is 16, then |a| is equal to :

• A. $2\sqrt2$
• B. $2\sqrt3$
• C. $4\sqrt2$
• D. $4$

Answer 1

Answer: (C)

$4\sqrt2$

Answer 2

The correct answer is (C) : $4\sqrt2$
Equation of tangent at vertex : $L ≡ x+y-a = 0$
Focus :F ≡ (a,a)
Perpendicular distance of L from F
$= |\frac{a+a-a}{\sqrt2}| = |\frac{a}{\sqrt2}|$
Length of latus rectum $= 4|\frac{a}{\sqrt2}|$
Given $4. |\frac{a}{\sqrt2}| = 16$
$⇒ |a| = 4\sqrt2$