Question

Assertion :If the equation $6x^2-42xy+60y^2-11x+10y+\lambda =0$ represents two straight lines, then $\lambda =10.$ Reason: The second degree equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represents a pair of straight lines if $abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$

• 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

Reason is true from theory.

$\therefore abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0....(\ast )$
Now $6x^2-42xy+60y^2-11x+10y+\lambda =0$

$\Rightarrow a=6,b=60,c=\lambda ,h=-21,g=-\frac{11}{2},f=5$
$\therefore$ By (*) we have

$\lambda =-10$

$\therefore$ Assertion (A) is false