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The slopes of the common tangents of the...

The slopes of the common tangents of the hyperbolas `(x^(2))/(9)-(y^(2))/(16)=1` and `(y^(2))/(9)-(x^(2))/(16)=1`, are

A

`+-2`

B

`+-1`

C

`+-1//2`

D

none of these

Text Solution

Verified by Experts

Given hyperbolas are :
`(x^(2))/(9)-(y^(2))/(16)=1`……..`(i)`
and
`(x^(2))/(16)-(y^(2))/(9)=-1`……`(ii)`
The equation of any tangent to `(i)` is
`y=mx+-sqrt(9m^(2)-16)`
If it touches `(ii)`, then
`9m^(2)-16=9-16m^(2)`[If `y=mx+c` touches `(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1` then `c^(2)=b^(2)-a^(2)m^(2)`]
`impliesm=+-1`
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