JEE MATHEMATICS MCQ: SYSTEM OF CIRCLES

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The number of circles belonging to the system of circles

2\left( {{x^2} + {y^2}} \right) + \lambda \;x - \left( {1 + {\lambda ^2}} \right)y - 10 = 0

and orthogonal to

{x^2} + {y^2} + 4x + 6y + 3 = 0,

View answer and explanation

Correct option: A

The correct answer is A (2). By finding the condition for orthogonality between the circles, a quadratic equation in

\lambda

is obtained, yielding two possible values for

\lambda

, hence two circles.

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