InterviewSolution
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InterviewSolution
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If the slope of one of the pairs of lines represented by equation `a^(3) x^(2) + 2hxy + b^(3) y^(2) = 0` is square of the other, then prove that `ab(a+ b) = - 2h. ` |
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Answer» `a^(3) x^(2) + 2hxy + b^(3) y^(2)= 0` `rArr b^(3) ((y)/(x))^(2) + 2h ((y)/(x)) + x^(3) = 0` Lines are `y = mx, where m = m_(1) and m_(2).` `rArr b^(3) m^(2) + 2hm + a^(3) = 0` (1) Given that slope of one line is square of the other line. So, roots are `alpha and alpha^(2)`. `rArr alpha a//b,` which satisfies the equation (1) So, `b^(3) (a^(2))/(b^(2)) + 2h (a)/(b) + a^(3) = 0` `rArr ab^(2) + a^(2) b+ 2h = 0` `rArr ab (a+b) = - 2h` |
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