99 Percentile Qs Bank for JEE MainMathematicsCircle
If the circle x 2 + y 2 + 2 a 1 x + c = 0 lies completely inside the circle x 2 + y 2 + 2 a 2 x + c = 0 , then
Options
- Aa 1 a 2 > 0 ,   c < 0
- Ba 1 a 2 > 0 ,   c > 0
- Ca 1 a 2 < 0 ,   c < 0
- Da 1 a 2 < 0 ,   c > 0
Correct answer
B. a 1 a 2 > 0 ,   c > 0
Step-by-step solution
We have, The circle x 2 + y 2 + 2 a 1 x + c = 0 , with centre C 1 - a 1 , 0 and circle x 2 + y 2 + 2 a 2 x + c = 0 , with centre C 2 - a 2 , 0 Equation of radical axis of the given circles is x = 0 . If one circle lies completely inside the other, then the centre of both circles should lie on the same side of radical axis and radical axis should not intersect the circles. ⇒ a 1 a 2 > 0 Putting x = 0 (equation of radical axis) to anyone of the circle, we get, y 2 + c = 0 . For imaginary roots, c > 0 (r