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 Δ PMN, then the correct expression(s) is(are)
= 1 – 
for x 1 > 1
for x 1 > 1
= 1+ 
for x 1 > 1
for y 1 > 0
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a,b,d)
Sol. 
Equation tangent to H at P is xx 1 – yy 1 = 1
= 
, m = 
now, vc 
= 
⇒ 
⇒ x 2 = 2x 1
So vr% , = x 1 + 
, 
, 
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