If the curves 4 x 2 + y 2 = 1 and a 2 x 2 + y 2 = 1 for suitable value of a cut on four concyclic points, then find the radius of the smallest circle passing through these 4 points

Question

If the curves 4 x 2 ​ + y 2 = 1 and a 2 x 2 ​ + y 2 = 1 for suitable value of a cut on four concyclic points, then find the radius of the smallest circle passing through these 4 points

TestHub · Accepted Answer

( 4 x 2 ​ + y 2 − 1 ) + λ ( a 2 x 2 ​ + y 2 − 1 ) = 0 x 2 ( 4 a 2 ( 1 + λ ) a 2 + 4 λ ​ ) + y 2 = 1 Clearly radius is 1 unit

Mathematics - Circle Question with Solution | TestHub

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