Question

The length of a focal chord of the parabola y2 = 4ax at a distance b from the vertex is c. Then

• A. 2a2 = bc
• B. a3 = b2c
• C. ac = b2
• D. b²c = 4a³

Answer 1

Answer: (D)

b²c = 4a³

Answer 2

Chord joining two points t1 and t2 is

(t1 + t2)y = 2x + 2at1t2

$\left| \frac{2at_{1}t_{2}}{\sqrt{4 + (t_{1} + t_{2})^{2}}} \right|$= b ... (1)

a (t1 – t2)2 = c ... (2)

By using (1) and (2), eliminate t1 & t2