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  • If the curves <img alt="\mathrm{\frac{x^2}{4}+y^2=1 \text { and } \frac{x^2}{a^2}+y^2=1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%7Bx%5E2%7D%7B4%7D&plus;y%

If the curves \mathrm{\frac{x^2}{4}+y^2=1 \text { and } \frac{x^2}{a^2}+y^2=1} for suitable value of a cut on four concyclic points, then the radius of the smallest circle passing through these 4 point is ________

Option: 1

0


Option: 2

2


Option: 3

1


Option: 4

4


Answers (1)

best_answer

\mathrm{\begin{aligned} & \therefore \left(\frac{x^2}{4}+y^2-1\right)+\lambda\left(\frac{x^2}{a^2}+y^2-1\right)=0 \\ &\Rightarrow x^2\left(\frac{a^2+4 \lambda}{4 a^2(1+\lambda)}\right)+y^2=1 \end{aligned}}

Clearly radius is 1 unit.

Posted by

Ajit Kumar Dubey

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