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Consider the hyperbola H:x^2-y^2=1 and a...

Consider the hyperbola `H:x^2-y^2=1` and a circile 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_1gt1andy_1gt0`.
The common langent to H and S intersects the x-axis at point
M. If (l,m) is the centroid of the triangle `trianglePMN`, then the
correct expression(s)is(are)

A

`(dl)/dx_1=1-1/(3x_1^2)`for`x_1gt1`

B

`(dm)/dx_1=x_1/(3(sqrt(x_1^2-1))` for `x_1gt`

C

`(dl)/dx_1=1+1/(3x^2)`for`x_1gt1`

D

`(dm)/dy_1=1/3` for `y_1gt0`

Text Solution

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The correct Answer is:
A, B, D
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