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NTA Abhyas JEE Main2020MathematicsCirclePractice

The two circles x 2 + y 2 = a x and x 2 + y 2 = c 2 c > 0 touch each other, if c a is equal to

Options

  1. A2
  2. B1 2
  3. C1
  4. DNone of these

Correct answer

C. 1

Step-by-step solution

The two circles touch each other internally as shown in the figure below For the circle x 2 + y 2 - 2 a x = 0 , the centre is at a 2 , 0 and radius is a 2 units. Also, the circle is passing through the origin. For the circle x 2 + y 2 = a 2 , the centre is at 0 , 0 and radius is c units From the figure, c = 2 a 2 = a Hence, c a = 1

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