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JEE Main201912 Apr 2019Evening ShiftMathematicsCircleActual

A circle touching the x - axis at ( 3 , 0 ) and making an intercept of length 8 on the y - axis passes through the point:

Options

  1. A3 , 10
  2. B2 , 3
  3. C3 , 5
  4. D1 , 5

Correct answer

A. 3 , 10

Step-by-step solution

Since circle touches the x-axis at 3 ,   0 , hence centre can be taken as 3 , α and radius = α Since y-intercept is 8, by applying Pythagorean theorem 3 2 + 4 2 = α 2 ⇒ α = 5 , - 5 Hence two circles are possible x - 3 2 + y - 5 2 = 25   and x - 3 2 + y + 5 2 = 25 . Clearly ( 3 ,   10 ) satisfies the given equation of circle.

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