InterviewSolution
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InterviewSolution
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There exist two points `P` and `Q` on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` such that `PObotOQ`, where `O` is the origin, then the number of points in the `xy`-plane from where pair of perpendicular tangents can be drawn to the hyperbola , isA. `0`B. `1`C. `2`D. infinite |
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Answer» Let `P(a sectheta_(1),btantheta_(1))` and `Q(a sectheta_(2),btantheta_(2))` be two points on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` such that `OPbotOQ` `implies(b)/(a)(tantheta_(1))/(sectheta_(1))xx(b)/(a)(tantheta_(2))/(sectheta_(2))=-1` `impliessintheta_(1)sintheta_(2)=-(a^(2))/(b^(2))` `impliesa^(2) lt b^(2)` The point on `xy`-plane from where perpendicular tangents are drawn to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` lie on the director circle `x^(2)-y^(2)=a^(2)-b^(2)`. For `a^(2) lt b^(2)` the director circle does not exist.So, there is no point in `xy`-plane. |
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