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JEE Main201910 Apr 2019Evening ShiftMathematicsCircleActual

The locus of the centres of the circles, which touch the circle, x 2 + y 2 = 1 externally, also touch the y -axis and lie in the first quadrant, is:

Options

  1. Ay = 1 + 2 x ,   x ≥ 0
  2. By = 1 + 4 x ,   x ≥ 0
  3. Cx = 1 + 2 y ,   y ≥ 0
  4. Dx = 1 + 4 y ,   y ≥ 0

Correct answer

A. y = 1 + 2 x ,   x ≥ 0

Step-by-step solution

Let, the centre of the circle whose locus is to be determined is P ( h ,   k ) and it touches y -axis in the first quadrant and we know that if a circle touches the y -axis, then its radius is equal to the absolute value of the x -coordinate of the centre. Hence, the radius of the circle is = h . Also, we know that if two circles touches externally, then the distance between their centres is equal to the sum of their radii. And, the centre and radius of a circle x 2 + y 2 = r 2 is 0 ,   0 and 1 respective

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