The locus of the point, tangents from which to the rectangu…

Maths Conic Sections Hyperbola Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

The locus of the point, tangents from which to the rectangular hyperbola x 2 – y 2 = a 2 contain an angle of 45 ° ° is

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

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

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

(x 2 + y 2 ) + a 2 (x 2 – y 2 ) = a 4

Text Solution

Verified by Experts

The correct answer is:

Let y = mx ± ± be two tangents and passing through (h, k). Then

(k – mk) 2 = m 2 a 2 – a 2 ⇒ ⇒ m 2 (h 2 – a 2 ) – 2khm + k 2 + a 2 = 0.

⇒ ⇒ m 1 + m 2 = and m 1 m 2 = , and tan45 0 =

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