JEE Advanced 2015 Paper 2 Mathematics Q12

Mathematics

Problem

Consider the hyperbola

H:x^2-y^2=1

and a circle

S

with center

N(x_2,0)

. Suppose that

H

and

S

touch each other at a point

P(x_1,y_1)

with

x_1>1

and

y_1>0

. The common tangent to

H

and

S

at

P

intersects the

x

-axis at point

M

. If

(l,m)

is the centroid of the triangle

\triangle PMN

, then the correct expression(s) is(are)

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