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 The centre of a circle S = 0 lies on 2x - 2y + 9 = 0 and S = 0 cuts orthogonally the circle x2 + y2 = 4. Then the circle must pass through the point

(A)  (1, 1)

(B)  (- 1/2, 1/2)

(C)  (5, 5)

(D)  ( -4, 4)

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Correct option  (B)(D)

Explanation:

Let S =  x2 + y2 + 2gx + 2fy + c = 0

∴ it cuts x2 + y2 = 4 orthogonally

⇒ c = 4

Moreover  - 2g + 2f + 9 = 0

∴  (- g, - f) satisfy the given equation) 

 S = x2 + y2 + 2gx + 2fy + 4 = 0

⇒ x2 + y2 + (2f + 9)x + 2fy + 4 = 0

⇒ (x2 + y2 + 9x + 4) + 2f (x + y) = 0

It is of the form S + λP = 0 and hence passes through the intersection of S = 0 and P = 0 which when solved give (-1/2, 1/2), (-4, 4).

Happy Diwali Wishes

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