﻿ The normal to the rectangular hyperbola xy = c2 at the point ‘t’ meets the curve again at point “t” such that : Kaysons Education

# The Normal To The Rectangular Hyperbola xy = c2 at The Point ‘t’ Meets The Curve Again At Point “t” Such That

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## Question

### Solution

Correct option is

t3t’ = –1

Any point P on xy = c2         ….. (1)

Similarly another point Q is . Diff. (1) w.r.t. x,

So equation of normal at P is

⇒ t3x – ty + (c – ct4) = 0                          …. (2)

Equation of line PQ is y – y1

Now (2) and (3) represent same line

⇒ x + ytt’ – c(t + t’) = 0                       …. (3)

⇒ t3t’ = –1

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