If a ≠ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay , then

Question

If a ≠ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay , then (A) d2 + (2b + 3c)2 = 0 (B) d2 + (3b + 2c)2 = 0 (C) d2 + (2b − 3c)2 = 0 (D) d2 + (3b − 2c)2 = 0

Tardigrade Admin · Accepted Answer

Points of intersection of given parabolas are

(0, 0)

and

(4 a, 4 a)

\Rightarrow

equation of line passing through these points is

y = x

On comparing this line with the given line

2 b x + 3 cy + 4 d = 0

, we get

d = 0

and

2 b + 3 c = 0 \Rightarrow (2 b + 3 c)^{2} + d^{2} = 0

.

Q. If $a \neq = 0$ and the line $2 b x + 3 cy + 4 d = 0$ passes through the points of intersection of the parabolas $y^{2} = 4 a x$ and $x^{2} = 4 a y$ , then

$d^{2} + (2 b + 3 c)^{2} = 0$

$d^{2} + (3 b + 2 c)^{2} = 0$

$d^{2} + (2 b - 3 c)^{2} = 0$

$d^{2} + (3 b - 2 c)^{2} = 0$

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

Q. If a=0 and the line 2bx+3cy+4d=0 passes through the points of intersection of the parabolas y2=4ax and x2=4ay , then

d2+(2b+3c)2=0

d2+(3b+2c)2=0

d2+(2b−3c)2=0

d2+(3b−2c)2=0