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If m is the slope of a tangent to the hy...

If m is the slope of a tangent to the hyperbola `(x^(2))/(a^(2)-b^(2))-(y^(2))/(a^(3)-b^(3)) =1` where `a gt b gt 1` when

A

`(a+b) m^(2)+ab ge (a+b)^(2)`

B

`(a+b)^(2)m+ab ge (a+b)`

C

`abm^(2)+(a+b)ge (a+b)^(2)`

D

`(a+b)m^(2)+a^(2)b^(2)ge (a+b)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
For hyperbola `(x^(2))/(A^(2))-(y^(2))/(B^(2)) =1` equation of tangent having slope m is
`rArr y = mx +- sqrt(A^(2)m^(2)-B^(2))`
where `A^(2)m^(2) -B^(2) ge 0`
`rArr m^(2) ge (B^(2))/(A^(2))`
`rArr m^(2) ge (a^(3)-b^(3))/(a^(2)-b^(2))`
`rArr (a+b)m^(2) ge a^(2) + ab + b^(2)`
`rArr (a+b) m^(2) + ab ge (a+b)^(2)`
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