(C) The general equation of a pair of straight lines is given by $Ax^{2}+2Hxy+By^{2}+2Gx+2Fy+C=0$. \\ For the pair of lines to be perpendicular,the su

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

Class 11 Mathematics Pair of straight lines Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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

MHT CET 2008 All MHT CET

A
$7/2$
B
$-19$
C
$-12$
D
$12$

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Pair of straight lines

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Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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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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