Published by:
CGP EDU Academic Team
Published on: August 13, 2026
P is a variable point on the hyperbola 
whose vertex is A (a, 0). The locus of the middle point of AP is
A
B
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
B
Let (x 1 , y 1 ) be the mid point of the variable chord AP (where A is fixed while P varies) of the hyperbola
.
Equation of the chord having (x 1 , y 1 ) as its mid points is 
(T = S 1 )
As it passes through the fixed point A (a, 0)
∴ ∴ 
⇒ ⇒ 
⇒ ⇒ 
⇒ ⇒ 
Hence locus of (x 1 , y 1 ) is 
.
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