Question

Assertion :Shortest distance between $|x|+|y|=2$ and $x^2+y^2=16$ is $4-\sqrt{2}$. Reason: Shortest distance between the two smooth curves lies along the common normal.

• 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 and Reason are correct.

Answer 1

The correct option is D Assertion is incorrect and Reason are correct.

From the figure, we observe that the shortest distance between $|x|+|y|=2$ and $x^2+y^2=16$ is along the axis, which is $4-2=2$.

Hence, Assertion is wrong.

Statement given in Reason is true for smooth curves.