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Q.

S(x, y) = 0 represents a circle. The equation S(x, 2) = 0 gives two identical solutions x = 1 and the equation S(1, y) = 0 gives two solutions y = 0, 2. Then equation of the circle is

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a

x² + y² + 2x – 2y + 1 = 0

b

2x² + 2y² – 4x – 4y + 5 = 0

c

x² + y²+ 3x – 2y + 1 = 0

d

x² + y² – 2x – 2y + 1 = 0

answer is A.

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Detailed Solution

$S (x, y) = x^{2} + y^{2} + 2 gx + 2 fy + c = 0 . Given thatS (x, 2) = x^{2} + 2 gx + 4 f + c + 4 = 0 has roots 1, 1 \Rightarrow - 2 g = 2 ∴ g = - 1 and 4 f + c + 4 = 1 4 f + c = - 3 . S (1, y) = y^{2} + 2 fy + 1 + 2 g + c = 0 has roots 0, 2 \Rightarrow - 2 f = 2 ∴ f = - 1, c = 1$

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