Question

The length of the tangent drawn from any point on the circle \( x^2 + y^2 + 2\lambda x + \mu = 0 \) to the circle \( x^2 + y^2 + 2\gamma x + \lambda = 0 \), where \( \mu \geq \lambda \), is:

• A. \( \sqrt{\mu - \lambda} \)
• B. \( \sqrt{\mu^2 - \lambda^2} \)
• C. \( \sqrt{\mu - \lambda^2} \)
• D. \( \mu + \lambda \)

Hint:

To find the length of the tangent from a point to a circle, use the formula involving the radius and the distance from the center.

Answer 1

The Correct Option is A

Step 1: Formula for the length of the tangent.
The length of the tangent from a point to a circle is given by: \[ l = \sqrt{(x_1^2 + y_1^2 - r^2)} \] By applying this to the given circles, we obtain the length of the tangent as \( \sqrt{\mu - \lambda} \).
Thus, the correct answer is (1).