Question

If $a ≠ 0$ and the line $2bx + 3cy + 4d = 0$ passes through the points of intersection of the parabolas $y^2 = 4ax$ and $x^2 = 4ay$ , then

• A. $d^2 + (2b + 3c)^2 = 0$
• B. $d^2 + (3b + 2c)^2 = 0$
• C. $d^2 + (2b − 3c)^2 = 0$
• D. $d^2 + (3b − 2c)^2 = 0$

Answer 1

Answer: (A)

Points of intersection of given parabolas are $(0, 0)$ and $(4a, 4a)$
$⇒$ equation of line passing through these points is $y = x$
On comparing this line with the given line $2bx + 3cy + 4d = 0$, we get $d = 0$ and $2b + 3c = 0 ⇒ (2b + 3c)^2 + d^2 = 0$.