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If the curves (x^2)/4+y^2=1 and (x^2)/(a...

If the curves `(x^2)/4+y^2=1` and `(x^2)/(a^2)+y^2=1` for a suitable value of `a` cut on four concyclic points, the equation of the circle passing through these four points is

A

`x^(2)+y^(2)=2`

B

`x^(2)+y^(2)=1`

C

`x^(2)+y^(2)=4`

D

none of these

Text Solution

Verified by Experts

The equation of conic through the point of intersection of given two ellipse is
`((x^(2))/(4)+y^(2)-1)+lambda((x^(2))/(a^(2))+y^(2)-1)=0`
or `x^(2)((1)/(4)+(lambda)/(a^(2)))+y^(2)(1+lamda)=1+lambda`
or `x^(2)((a^(2))/(4a^(2)(1+lambda)))+y^(2)=1`
Therefore , the circle is `x^(2)+y^(2)=1`
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