The normal to the rectangular hyperbola xy = c 2 at the poi…

Maths Conic Sections Hyperbola Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The normal to the rectangular hyperbola xy = c 2 at the point 't' meets the curve again at a point 't' such that

t 3 t' = -1

t 2 t' = -1

tt' = -1

None of these

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The correct answer is:

The equation of the normal to xy = c 2 at the point 't' is

ty = t 3 x + c - ct 4 or t 3 x - ty + c - ct 4 = 0 ... (1)

Now, the equation of the line joining 't' and 't' is

⇒ ⇒

⇒ ⇒ ytt' - ct' = -x + ct

⇒ ⇒ x + ytt' - c(t + t') = 0

Since (1) and (2) represent the same line,

∴ ∴ , on comparing the coefficient of x and y, we get

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