Question

The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is
(A) 3√2 (B) 3
(C) 2 (D) 2√2

Answer 1

Option (B) 3 is the correct answer

Answer 2

The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is :

(D) 2√2

• The radius of the circle can be calculated as follows:

• We know that, Equation of circle can be represented as :

        (x−1)² + (y−1)² + λ(x−y) = 0

• As per the question, passes through (1,3),

• Thus, 16 + λ(4) = 0

                             λ = −4

• So (x−1)² + (y−1)² − 4(x−y) = 0

        x² + y² − 6x + 2y + 2 = 0

• Thus, r = 2√2

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