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AP EAMCET202119 Aug 2021Evening ShiftMathematicsCircleActual

If a foot of the normal from the point ( 4 , 3 ) to a circle is ( 2 , 1 ) and 2 x - y - 2 = 0 is a diameter of the circle, then the equation of circle is

Options

  1. Ax 2 + y 2 + 2 x + 1 = 0
  2. Bx 2 + y 2 + 2 x − 1 = 0
  3. Cx 2 + y 2 − 2 x − 1 = 0
  4. D2 x 2 + y 2 − 2 x − 1 = 0

Correct answer

C. x 2 + y 2 − 2 x − 1 = 0

Step-by-step solution

Given, the normal from the point 4 ,   3 to a circle is 2 ,   1 . So, the equation of this normal is y - 1 = 3 - 1 4 - 2 x - 2   ⇒   y = x - 1     . . . 1 , As, the normal at any point to the circle passes through its centre. And, we have a given diameter 2 x - y - 2 = 0       . . . 2 Hence, the centre of the circle is the point of intersection of 1 and 2 . Solving equations 1 and 2 , the centre is 1 ,   0 . And, the radius is equal to the distance between poi

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