Question

Assertion :The area of the ellipse $2x^2+3y^2=6$ will be more than the area of the circle $x^2+y^2-2x+4y+4=0$ Reason: The length of the semi-major axis of ellipse $2x^2+3y^2=6$ is more than the radius of the circle $x^2+y^2-2x+4y+4=0$

• 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. Assertion is incorrect, Reason is correct

Answer 1

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

The ellipse is $\frac{x^2}{3}+\frac{y^2}{2}=1$ and the circle is ${(x-1)}^2+{(y+2)}^2=1$

Area of ellipse $=\pi \sqrt{3}\sqrt{2}=\sqrt{6}\pi$ and area of circle

$=\pi .1^2=\pi .$

Assertion is true.

The reason $R$ is true in this particular example.

In general this may not be true.

Consider the ellipse

$\frac{x^2}{16}+\frac{y^2}{1}=1$ and the cirlce $x^2+y^2=9.$

We note that length of semi-major axes of ellipse i.e., $4$ is greater than radius of the circle but the area of ellipse $=4\times 1\times \pi$ and area circle $=9\pi .$

$\to$ area of ellipse is not greater then the area of circle.

Thus, $A$ is true but does not follow from $R.$