Question

Assertion :The lines $(a+b)x+2(a-b)y=2a$ are concurrent at the point $(1,\frac{1}{2})$ Reason: The lines $x+2y-2=0$ and $x-2y=0$ intersect at the point $(1,\frac{1}{2})$

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

The reason is correct and the lines in assertion can be written as

$a(x+2y-2)+b(x-2y)=0$

which pass through the point of intersection $(1,1/2)$ of the lines $x+2y-2=0$ and $x-2y=0$ and hence assertion is correct.