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NTA Abhyas JEE Main2020MathematicsCirclePractice

If the circle x - a 2 + y 2 = 25 intersects the circle x 2 + ( y - b ) 2 = 16 in such a way that the length of the common chord is 8 units, then the value of a 2 + b 2 is

Correct answer

9

Step-by-step solution

The equation of the common chord is - 2 a x + a 2 + 2 b y - b 2 = 9 which passes through 0 , b i.e. 0 2 + a 2 + 2 b 2 - b 2 = 9 ⇒ a 2 + b 2 = 9

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