If the line 2 b x+3 c y+4 d=0 passes through the points of intersection of y^2=4 a x and x^2=4 a y , then

Step-by-step solution

Given parabola, we have x^2=4 a y and y^2=4 a x Intersection point of these two parabolas are (0,0) and (4 a, 4 a) . Given that, 2 b x+3 c y+4 d=0 passes through point of intersection. Case I If it passes through (0,0) , we obtain aligned 2 b(0)+3 c(0)+4 d & =0 d & =0 aligned Case II If it passes through (4 a, 4 a) , we obtain aligned 2 b(4 a)+3 c(4 a)+4(0) & =0 (2 b+3 c)(4 a)=0 2 b+3 c & =0 aligned From Eqs. (i) and (ii), we get d^2+(2 b+3 c)^2=0