Question
Question: If a ¹ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas ...
If a ¹ 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 + (3b – 2c)2 = 0
B
d2 + (3b + 2c)2 = 0
C
d2 + (2b – 3c)2 = 0
D
d2 + (2b + 3c)2 = 0
Answer
d2 + (2b + 3c)2 = 0
Explanation
Solution
The two parabolas intersect at (0, 0) and (4a, 4a). The equation of their common chord must be y = x which must be same as given line
2bx + 3ay + 4d = 0
̃ 2b = – 3c, d = 0
̃ (2b + 3c)2 + d2 = 0