Published by:
CGP EDU Academic Team
Published on: August 14, 2026
AB is a chord to the curve S ≡ x 2 – y 2 – 16 = 0 with A (4, 0) and C is a point on line segment AB such that AC : AB = 1 : 2 then find the locus of C.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
x 2 – y 2 – 4x = 0
Sol.
x 2 – y 2 = 16
(4sec θ , 4 tan θ )
2h = 4 + 4 sec θ
2k = 4 tan θ
x = 2 + 2 sec θ
y = 2 tan θ
1 + tan 2 θ = sec 2 θ
1 + 
4 + y 2 = (x – 2) 2 ⇒ (x – 2) 2 – y 2 = 4 ⇒ x 2 – y 2 – 4x = 0
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