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Hyperbola

Section: Mathematics

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Question : 8

Total: 15

Consider the hyperbola H:x2−y2=1 and a circle S with center N(x2,0).Suppose that H and S touch each other at a point P(x_1,y_1) with x1>1 and y1>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 ∆PMN,then the correct expression(s) is (are)

[JEE Adv 2015 P2]

dl
dx1
=1−
1
3x12
for x1>1
dm
dx1
=
x1
3(√x12−1)
for x1>1
dl
dx1
=1+
1
3x12
for x1>1
dm
dy1
=
1
3
for y1>0

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