Question

Assertion :The equation $2x^2+3xy-2y^2+5x-5y+3=0$ represents a pair of perpendicular straight lines. Reason: A pair of lines given by $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ are perpendicular, if $a+b=0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

$2x^2+3xy-2y^2+5x-5y+3=0$
Represent pair of lines if
$\left|\begin{array}{ccc}2& \frac{3}{2}& \frac{5}{2}\\ \frac{3}{2}& -2& -\frac{5}{2}\\ \frac{5}{2}& -\frac{5}{2}& 3\end{array}\right|=0$
$\Rightarrow 2(\frac{25}{4}+6)-\frac{3}{2}(-\frac{25}{4}-\frac{9}{2})+\frac{5}{2}(-5-\frac{15}{4})=0$
$\Rightarrow \frac{25}{2}+12+\frac{75}{8}+\frac{27}{4}-\frac{25}{2}-\frac{75}{8}=0$
But $\Rightarrow \frac{75}{4}\ne 0$