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The value(s) of a for which two curves `y=ax^(2)+ax+(1)/(24)andx=ay^(2)+ay+(1)/(24)` touch each other is/areA. `(2)/(3)`B. `(1)/(3)`C. `(3)/(2)`D. `(1)/(2)` |
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Answer» Correct Answer - A::C 1,3 The two curves are symmetric about the line y=x. Hence, they touch each other on y=x. So, the point of contact is `(alpha,alpha)`. From any of the equations, we get `alpha=aalpha^(2)+aalpha+(1)/(24)` `or24aalpha^(2)+24alpha(a-1)+1=0` This equation should have Identical roots. `rArrD=0` `rArr(24)^(2)(a-1)^(2)-4(24a)=0` `rArr6a^(2)-13a+6=0` `rArr(2a-3)(3a-2)=0` `rArra=3//2,2//3` |
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