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The angle between pair of tangents to th...

The angle between pair of tangents to the curve `7x^(2)-12y^(2)=84` from the point `M(1,2)` is

A

`2tan^(-1)"(1)/(2)`

B

`2tan^(-1)2`

C

`2(tan^(-1).(1)/(3)+tan^(-1).(1)/(2))`

D

`2tan^(-1)3`

Text Solution

Verified by Experts

The equation of the director circles of the given byperbola is
`x^(2)+y^(2)=12-7` or `x^(2)+y^(2)=5`
Clearly, the point `M(1,2)` lies on the director circle `x^(2)+y^(2)=5`.
So, the angle between the tangents to the hyperbola drawn from `M(1,2)` is right angle.
Now,
`2(tan^(-1).(1)/(3)+tan^(-1).(1)/2)=2tan^(1)(((1)/(3)+(1)/(2))/(1-(1)/(3)xx(1)/(2)))=2tan^(1)1=(pi)/(2)`
Hence, option `(c )` is correct.
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