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AP EAMCET202023 Sep 2020Morning ShiftMathematicsCircleActual

If one end of the diameter of x 2 + y 2 - 2 x - 6 y - 15 = 0 is 4 , 1 , then the co-ordinates of the other end is

Options

  1. A( 5 , - 2 )
  2. B( - 2 , 5 )
  3. C1 , 3
  4. D- 2 , - 5

Correct answer

B. ( - 2 , 5 )

Step-by-step solution

Given: The equation of the circle is x 2 + y 2 - 2 x - 6 y - 15 = 0 ⇒ x - 1 2 + y - 3 2 - 25 = 0 So the centre of the circle is 1 , 3 and its radius is 5 . We know that the centre is mid-point of the diameter. Also one end of the diameter is 4 , 1 and let other end be a , b . By mid point formula, 1 = a + 4 2 and 3 = b + 1 2 ⇒ a = - 2 and b = 5 So the other end of the diameter is - 2 ,   5 .

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