Question

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

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

Answer 1

Answer: (A)

Both assertion and reason are correct and reason is the correct explanation for the assertion.

Assertion : $2x^2+3xy-2y^2+5x-5y+3=0$

$tan\theta =|\frac{2\sqrt{h^2-ab}}{a+b}|$

Given $Q={90}^{\circ },$ then $a+b=0$

And $a=2,b=-2$

in given equation

So,$a+b=0$ True

Reason (R): pair of

lines given by

$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$

Are perpendicular then, if $a+b=0$

$tan\theta =|\frac{2\sqrt{h^2-ab}}{a+b}|$

$\theta ={90}^{\circ }$ then $a+b=0$ True