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Question

The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y – 4x + 3 = 0, is


A
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B
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C
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D
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Solution

The correct option is B

Required circle is s+λL=0

(x2)(x4)+(y3)(y5)+λ(xy+1)=0

x2+y2+(λ6)x(8+λ)y+23+λ=0

centre = (6λ2,8+λ2)

centre lies on y - 4x + 3 = 0

(8+λ2)4(6λ2)+3=08+λ24+4λ+6=0λ=2
Required circle is
x2+y24x10y+25=0


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