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Hi Siddharth,
The Area of an ellipse is Πab.
This is a very nice question, where if you note in the given ellipse equation:
If you replace "y" by "x" you'd get the same ellipse equation.
And hence the ellipse is summetric about the line y=x.
Also if you replace "x" by "-y" and "y" by "-x" you will again get the same ellipse equation.
And hence the ellipse is also symmetric about the line y=-x.
So, now we conclude that the given ellipse is centred at the origin, with it's axes as y=x, and y=-x.
Now we start solving the problem.
Solve the ellipse eqn with y=x, you will get two points of intersection viz (1/root[10],1/root[10]) and (-1/root[10,-1/root[10])
Next solve the ellipse eqn with y=-x. Points of intersection (1/root[2],-1/root[2]) and (-1/root[2],1/root[2])
So now distance between one of the pair is "a" and the distance between other pair is "b"
So a=2/root(5)
and b=2.
So now pi(ab) = given value. And hence you will get "A".
Best Regards,
Ashwin (IIT Madras).
I did not get the full question but I have found the area of the given ellipse and it is - pi/root(20)
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