Home Maths Conic Sections Parabola If a ≠ 0 and the line 2bx + 3cy + 4d = 0 pas…
Maths Conic Sections Parabola Single Correct MCQ
Published on: August 14, 2026

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 + (3b – 2c)2 = 0
B
d2 + (3b + 2c)2 = 0
C
d2 + (2b – 3c)2 = 0
D
d2 + (2b + 3c)2 = 0

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Text Solution

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The correct answer is:
D

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

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