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Maths Conic Sections Hyperbola Single Correct MCQ

Published on: August 13, 2026

A normal to the hyperbola – = 1 meets the axis in A and B the line AL and BL are drawn at Right angle to the axis and meet at L then locus of L is -

a 2 x 2 – b 2 y 2 = (a 2 + b 2 ) 2

b 2 x 2 – a 2 y 2 = (a 2 + b 2 ) 2

4(a 2 x 2 – b 2 y 2 ) = (a 2 + b 2 ) 2

None of these

Text Solution

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The correct answer is:

Normal to the hyperbola is

ax cos θ + by cot θ = a 2 + b 2 Putting y = 0 and x = 0

We get A , B

line through A, perpendicular to the x-axis is

x = sec θ

line through B, perpendicular to the y-axis is y

= tan θ

So intersection of these point is L

 sec

2 θ – tan 2 θ = 1

⇒ a 2 x 2 – b 2 y 2 = (a 2 + b 2 ) 2 .

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