Let the mirror image of a circle c_ 1 : x^ 2 + y^ 2 - 2x - 6y + = 0 in line y = x + 1 be c_ 2 : 5x^ 2 + 5y^ 2 + 10gx + 10fy + 38 = 0. If r is the radius of circle c_ 2 , then + 6r^ 2 is equal to _____.

JEE Main 2022 Mathematics question

Let the mirror image of a circle : in line y = x + 1 be : . If r is the radius of circle , then is equal to .

Answer: 12

Solution

The centre of is (1, 3), and its image in the line x − y + 1 = 0 is given by ( − 1)/1 = ( − 3)/(−1) = −2(1 − 3 + 1)/(1 + 1) = 1, so (, , 2). So has centre (2,

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Question ID VK-035165