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AP EAMCET202119 Aug 2021Evening ShiftMathematicsCircleActual

Find the equation of a circle whose radius is 5 units and passes through two points on the x axis which are at a distance of 4 units from the origin.

Options

  1. Ax 2 + y 2 − 6 x − 25 = 0
  2. Bx 2 + y 2 − 6 y − 25 = 0
  3. Cx 2 + y 2 + 6 y − 16 = 0
  4. Dx 2 + y 2 + 6 x − 16 = 0

Correct answer

C. x 2 + y 2 + 6 y − 16 = 0

Step-by-step solution

As, given the circle is passing through points 4 ,   0 and - 4 ,   0 , So, the centre must lie on y - axis. Let, the coordinate of the centre is 0 ,   c , Hence, the radius, 0 - 4 2 + c - 0 2 = 5   ⇒   c = ± 3 , ⇒ the co ordinate of the centre is 0 ,   3   or   0 , - 3 . So, the equation of such circles are x - 0 2 + y - 3 2 = 5 2   ⇒   x 2 + y 2 - 6 y - 16 = 0 or x - 0 2 + y + 3 2 = 5 2   ⇒   x 2 + y 2 + 6 y - 16 = 0

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