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A circle passes through - 2 , 4 and touches the y - axis at 0 , 2 . Which one of the following equations can represent a diameter of this circle ?

Options

  1. A2 x - 3 y + 10 = 0
  2. B3 x + 4 y - 3 = 0
  3. C4 x + 5 y - 6 = 0
  4. D5 x + 2 y + 4 = 0

Correct answer

A. 2 x - 3 y + 10 = 0

Step-by-step solution

As y - axis is tangent to the circle therefore the centre of the circle would be x , 2 and distance of centre from 0 , 2 and - 2 , 4 should be equal. ∴ h 2 + 0 2 = h + 2 2 + 2 2 ⇒ h 2 = h 2 + 4 h + 4 + 4 ⇒ h = - 2 Hence, centre is - 2 , 2 . ∴ 2 x - 3 y + 10 = 0 is the diameter, as centre lies on it.

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