InterviewSolution
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InterviewSolution
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The angle between pair of tangents to the curve `7x^(2)-12y^(2)=84` from the point `M(1,2)` isA. `2tan^(-1)"(1)/(2)`B. `2tan^(-1)2`C. `2(tan^(-1).(1)/(3)+tan^(-1).(1)/(2))`D. `2tan^(-1)3` |
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Answer» 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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