Question

Assertion :The differential equation of the family of hyperbolas with asymptotes as the lines $x+y=1$ & $x-y=1$ given by $y\frac{dy}{dx}=x-1$ Reason: The eccentricity of rectangular hyperbola is $\sqrt{2}$

• 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Given equations are $x+y=1,x-y=1$
The point of intersection of these lines gives the centre of hyperbola so solving the equations we get $x=1,y=0$
$\therefore$ Equation of hyperbola is given by
$\frac{{(x-1)}^2}{a^2}-\frac{{(y-0)}^2}{a^2}=1$
$\Rightarrow$ $2(x-1)-2y\frac{dy}{dx}=0$
$\Rightarrow$ $2y\frac{dy}{dx}=x-1$
Reason is obviously correct but it is not explanation of Assertion.
Hence, option 'B' is correct.