Question

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Answer 1

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option no. 1) x²+y²-3x+1

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Answer 2

Answer:

Option(2)

Step-by-step explanation:

(i) S₁ = x² + y² - 6 = 0

(ii) S₂ = x² + y² - 6x + 8 = 0

Equation of circle passing through the point of intersection of the circles S₁ and S₂ is taken as,

⇒ S₁ + K(S₂ - S₁) = 0

⇒ x² + y² - 6 + K(x² + y² - 6x + 8 - x² - y² + 6) = 0

⇒ x² + y² - 6 + K(-6x + 14) = 0

Given points are (1,1).

⇒ -4 + K(8) = 0

⇒ -4 + 8K = 0

⇒ -4 = -8K

⇒ K = 1/2

Hence, the required equation is:

⇒ 2x² + 2y² - 12 + (x² + y² - 6x + 8 - x² - y² + 6) = 0

⇒ 2x² + 2y² - 12 + x² + y² - 6x + 8 - x² - y² + 6 = 0

⇒ 2x² + 2y² - 6x + 2 = 0

⇒ x² + y² - 3x + 1 = 0.

Therefore, the required equation is x² + y² - 3x + 1 = 0.

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