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CGP EDU Academic Team
Published on: August 14, 2026
The normal to the hyperbola 4x 2 - 9y 2 = 36 meets the axes in M and N and the lines MP, NP are drawn at right angles to the axes. The locus of P is the hyperbola.
Text Solution
Verified by ExpertsThe correct answer is:
A
The given hyperbola can be written in the form
.
The equation of any normal to the given hyperbola is 
.
It meets x-axis in M 
and y-axis in N 
.
Let the coordinates of P be (x 1 , y 1 ).
Since MP ⊥ ⊥ NP, x 1 = NP = 
sec θ θ , y 1 = MP = 
tan θ θ
∴ ∴ sec θ θ = 
and tan θ θ = 
.
⇒ ⇒ 
( 
sec 2 θ θ - tan 2 θ θ = 1)
Hence the locus of (x 1 , y 1 ) is 9x 2 - 4y 2 = 169.
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