Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If the normal at P to the rectangular hyperbola x 2 – y 2 = 4 meets the axis in G and g and C is the centre of the hyperbola, then-
A
2PG = PC
B
Pg = PC
C
PG = Pg
D
Gg = 2PC
Text Solution
Verified by ExpertsThe correct answer is:
D
Let P(x 1 , y 1 ) be any point on the hyperbola
x 2 – y 2 = 4, then equation of the normal at P is y – y 1 = – 
(x – x 1 ) ⇒ x 1 y + y 1 x = 2x 1 y 1 .
Then coordinates of G are (2x 1 , 0) and of g are (0, 2y 1 )
So that PG = 
= 
= PC
Pg = 
= 
= PC and
Gg = 
= 2 
= 2PC.
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