InterviewSolution
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InterviewSolution
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The number of normal (s) of a rectangular hyperbola which can touch its conjugate is equal to |
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Answer» Correct Answer - C Normal to hyperbola `xy = c^(2)` at `(ct, (c )/(t))` is `y - (c )/(t) = t^(2) (x-ct)` Solving with `xy =- c^(2)`, we get `rArr x {(c )/(t) + t^(2) (x-ct)} +c^(2) =0` `rArr t^(2) x^(2) + ((c )/(t)-ct^(3)) x +c^(2) =0` Since line touches the curve, above equation has equal roots `:. Delta = 0, ((1)/(t)-t^(3))^(2) - 4t^(2) =0` `rArr (1-t^(4))^(2) - 4t^(4) =0` `rArr t^(2) = (2=- sqrt(8))/(2)` or `(-2 +- sqrt(8))/(2)` `rArr t^(2) =1 + sqrt(2)` or `-1 + sqrt(2)` Thus four such values of t are possible |
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