The circle through the two points (–2, 5), (0, 0) and intersecting x2 + y2 – 4x + 3y – 1 = 0 orthogonally is

circle s = 0 passes through (0, 0) and (−2,5)⇒C=0 and −4g+10f=−29S = 0 cuts given circle orthogonally⇒−4g+3f=−1 solving f=−4,g=−114∴ circle is 2x2+2y2−11x−16y=0

The circle through the two points (–2, 5), (0, 0) and intersecting x2 + y2 – 4x + 3y – 1 = 0 orthogonally is

circle s = 0 passes through (0, 0) and (−2,5)⇒C=0 and −4g+10f=−29S = 0 cuts given circle orthogonally⇒−4g+3f=−1 solving f=−4,g=−114∴ circle is 2x2+2y2−11x−16y=0

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The circle through the two points (–2, 5), (0, 0) and intersecting x² + y² – 4x + 3y – 1 = 0 orthogonally is

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2x² + 2y² – 11x – 16y = 0

x² + y² + 2x – 5y = 0

2x² + 2y² + 2x – 5y + 1 = 0

x² + y² – 4x – 4y = 0

answer is A.

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Detailed Solution

circle s = 0 passes through (0, 0) and $(- 2, 5) \Rightarrow C = 0 and - 4 g + 10 f = - 29$
S = 0 cuts given circle orthogonally
$\begin{array}{l} \Rightarrow - 4 g + 3 f = - 1 solving f = - 4, g = \frac{- 11}{4} \\ ∴ circle is 2 x^{2} + 2 y^{2} - 11 x - 16 y = 0 \end{array}$