Question

Assertion :The differential equation of all non-vertical lies in a plane is $\frac{d^{2}y}{d{x}^2}=0$ Reason: The general equation of all non-vertical lines in a plane is given by $ax+by=2(b\ne 0)$

• 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. 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 general equation of all non-vertical lines in a plane is $ax+by=2(b\ne 0)$
Now $ax+by=2$
$\Rightarrow$ $a+b\frac{dy}{dx}=0$, $b\frac{d^{2}y}{d{x}^2}=0$ or $\frac{d^{2}y}{d{x}^2}=0$ (as $b\ne 0$)
Therefore, the differential equation is $\frac{d^{2}y}{d{x}^2}=0$.