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From point `P(8,27)` tangents PQ and PR are drawn to the ellipse `(x^(2))/(4)+(y^(2))/(9)=1.` Then, angle subtended by QR at origin isA. `tan ^(-1)""(2sqrt6)/(65)`B. `tan ^(-1)""(4sqrt6)/(65)`C. `tan^(-1)""(8sqrt2)/(65)`D. None of these |
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Answer» Correct Answer - D Equation of chord of contact QR is `8*x/4+27*y/9=1` `implies2x+3y=1" "...(i)` Now, equation of the pari of lines passing through origin and points Q, R given by `((x^(2))/(4)+(y^(2))/(9))=(2x+3y)^(2)` `implies9x^(2)+4y^(2)=36(4x^(2)+12xy+9y^(2))` `implies135x^(2)+432xy+320y^(2)=0` `therefore` Required angle is `=tan ^(-1)""(2sqrt((216)^(2)-135*320))/(455)` `=tan ^(-1)""(8sqrt(2916-2700))/(455)` `=tan ^(-1)""(8sqrt216)/(455)` `=tan ^(-1)""(48sqrt6)/(455)` |
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