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Question: The circle x<sup>2</sup> + y<sup>2</sup> + 2a<sub>1</sub>x + b = 0 lies completely inside the circle...

The circle x2 + y2 + 2a1x + b = 0 lies completely inside the circle x2 + y2 + 2a2 x + b = 0, then

A

a1a2> 0, b < 0

B

a1a2> 0, b > 0

C

a1a2< 0, b < 0

D

a1a2< 0, b > 0

Answer

a1a2> 0, b > 0

Explanation

Solution

Equation of radical axis of the given circles is x = 0. If one circle lies completely inside the other, then centre of both circles should lie on the same side of radical axis and the radical axis should not intersect the circles.

Here, (– a1) (– a2) > 0

Ž a1a2 > 0 and y2 + b should have imaginary roots.

Ž a1a2 > 0 and b > 0.