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Tangents are drawn to the hyperbola `x^2/9-y^2/4=1` parallet to the sraight line `2x-y=1.` The points of contact of the tangents on the hyperbola are (A) `(2/(2sqrt2),1/sqrt2)` (B) `(-9/(2sqrt2),1/sqrt2)` (C) `(3sqrt3,-2sqrt2)` (D) `(-3sqrt3,2sqrt2)`A. `(3sqrt(3),-2sqrt(2))`B. `(-9/(2sqrt(2)),-1/(sqrt(2)))`C. `(9/(2sqrt(2)),1/(sqrt(2)))`D. `(-3sqrt(3),2sqrt(2))` |
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Answer» Correct Answer - B::C Slope of tangent `=2` the tangents are `y=2x+-sqrt(9xx4-4)` i.e. `2x-y=+-4sqrt(4)` `impliesx/(2sqrt(2))-y/(4sqrt(2))=1` and `(-x)/(2sqrt(2))+y/(4sqrt(2))=1` Comparing it with `("xx"_(1))/9-(yy_(1))/4=1` we get point of contact as `(9/(2sqrt(2)),1/(sqrt(2)))` and `(-9/(2sqrt(2)),1/(sqrt(2)))` |
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