The tangent to the hyperbola at point intersects the -axis at and the -axis at

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The tangent to the hyperbola

xy = c^2

at point

P(t)

intersects the

X

-axis at

T

and the

Y

-axis at

T'

. The normal to the hyperbola at

P(t)

intersects the

X

-axis at

N

and the

Y

-axis at

N'

. The areas of the triangles

PNT

and

PN'T'

are

\Delta

and

\Delta'

respectively, then

\frac{1}{\Delta} + \frac{1}{\Delta'}

is (1) equal to 1 (2) depends on

t

(3) depends on

c

(4) equal to 2