| Statement-1: The area of the ellipse \[2{{x}^{2}}+3{{y}^{2}}=6\] is more than the area of the circle \[{{x}^{2}}+{{y}^{2}}-2x+4y+4=0.\] |
| Statement-2: If the length of the major axis of an ellipse is more than the diameter of a circle then the area of the ellipse will be more than the area of the circle. |
A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is false.
D) Statement-1 is false, Statement-2 is true.
Correct Answer: C
Solution :
For ellipse \[a=\sqrt{3},b=\sqrt{2}\]\[\Rightarrow \]area\[=\pi ab=\sqrt{6}\pi \] For circle \[r=1\Rightarrow \]area\[=\pi {{(r)}^{2}}=\pi \]. Second statement is not necessarily true.
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