InterviewSolution
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InterviewSolution
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From any point to the hyperbola `^2/a^2-y^2/b^2=1`, tangents are drawn to thehyperbola `x^2/a^2-y^2/b^2=2` The area cut off bythe chord of contact on the regionbetween the asymptotes is equal toA. `a//2`B. `ab`C. `2ab`D. `4ab` |
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Answer» Correct Answer - D Let `P(x_(1),y_(1))` be a point on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` The chord of contact of tangents from P to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=2` is given by `(x x_(1))/(a^(2))-(yy_(1))/(b^(2))=2" "(1)` The equation of the asymptotes are `(x)/(a)-(y)/(b)=0` `and (x)/(a)+(y)/(b)=0` the points of intersection of (1) with the two asymptotes are given by `x_(1)=(2)/((x_(1)//a)-(y_(1)//b)),y_(1)=(2b)/((x_(1)//a)-(y_(1)//b))` `x_(2)=(2)/((x_(1)//a)-(y_(1)//b)),y_(2)=(-2b)/((x_(1)//a)-(y_(1)//b))` `"Area of the said triangle"=(1)/(2)|x_(1)y_(2)-x_(2)y_(1)|` `=(1)/(2)|-(4abxx2)/((x_(1)^(2)//a^(2))-(y_(1)^(2)//b^(2)))|=4ab` |
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