The equation 12x^2 + 7xy + ay^2 + 13x - y + 3 | vedclass

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(C) The general equation of a pair of straight lines is given by $Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0$.Comparing this with the given equation $12x^

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$-12$

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(C) The general equation of a pair of straight lines is given by $Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0$.Comparing this with the given equation $12x^2 + 7xy + ay^2 + 13x - y + 3 = 0$,we get $A = 12$ and $B = a$.For a pair of lines to be perpendicular,the sum of the coefficients of $x^2$ and $y^2$ must be zero,i.e.,$A + B = 0$.Substituting the values,we get $12 + a = 0$.Therefore,$a = -12$.

The equation $12x^2 + 7xy + ay^2 + 13x - y + 3 = 0$ represents a pair of perpendicular lines. Then the value of $a$ is

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