If the circle and intersect orthogonally, then is
- A.or
- B.or
- C.or
- D.or
Show answer and solution
Correct option: A
Solution
Two circles intersect orthogonally when 2g₁g₂ + 2f₁f₂ = c₁ + c₂.
For the first circle: g₁ = 1, f₁ = k, c₁ = 6.
For the second circle: g₂ = 0, f₂ = k, c₂ = k.
Applying the condition: 2(1)(0) + 2(k)(k) = 6 + k, which gives 2k² = 6 + k, so 2k² - k - 6 = 0.
Factoring: (2k + 3)(k - 2) = 0, giving k = 2 or k = -3/2.
For the first circle: g₁ = 1, f₁ = k, c₁ = 6.
For the second circle: g₂ = 0, f₂ = k, c₂ = k.
Applying the condition: 2(1)(0) + 2(k)(k) = 6 + k, which gives 2k² = 6 + k, so 2k² - k - 6 = 0.
Factoring: (2k + 3)(k - 2) = 0, giving k = 2 or k = -3/2.
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