If ax^2+6xy+by^2-10x+10y-6=0 represents a pai | vedclass

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(B) The given equation of the pair of lines is $ax^2+6xy+by^2-10x+10y-6=0$.Comparing this with the general equation $Ax^2+2Hxy+By^2+2Gx+2Fy+C=0$,we ge

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$4$

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(B) The given equation of the pair of lines is $ax^2+6xy+by^2-10x+10y-6=0$.Comparing this with the general equation $Ax^2+2Hxy+By^2+2Gx+2Fy+C=0$,we get $A=a, H=3, B=b, G=-5, F=5, C=-6$.For the equation to represent a pair of lines,the determinant must be zero:$\begin{vmatrix} a & 3 & -5 \ 3 & b & 5 \ -5 & 5 & -6 \end{vmatrix} = 0$$a(-6b-25) - 3(-18+25) - 5(15+5b) = 0$$-6ab - 25a - 21 - 75 - 25b = 0$$-6ab - 25(a+b) - 96 = 0$.Since the lines are perpendicular,the coefficient of $x^2$ plus the coefficient of $y^2$ must be zero,so $a+b=0$,which implies $b=-a$.Substituting $b=-a$ into the equation:$-6a(-a) - 25(a-a) - 96 = 0$$6a^2 - 96 = 0$$6a^2 = 96$$a^2 = 16$$|a| = 4$.

If $ax^2+6xy+by^2-10x+10y-6=0$ represents a pair of perpendicular lines,then the value of $|a|$ equals

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