Mathematics

Mathematics

Problem

The points of intersection of the line ax+by=0ax + by = 0, (a≠b)(a \neq b) and the circle x2+y2−2x=0x^2 + y^2 - 2x = 0 are A(α,0)A(\alpha, 0) and B(1,β)B(1, \beta). The image of the circle with ABAB as a diameter in the line x+y+2=0x + y + 2 = 0 is (2023 Main, 25 Jan I) (a) x2+y2−5x−5y+12=0x^2 + y^2 - 5x - 5y + 12 = 0 (b) x2+y2+3x+5y+8=0x^2 + y^2 + 3x + 5y + 8 = 0 (c) x2+y2+5x+5y+12=0x^2 + y^2 + 5x + 5y + 12 = 0 (d) x2+y2+3x+3y+4=0x^2 + y^2 + 3x + 3y + 4 = 0

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