Question

The length of the tangent drawn from the point \( \left(\frac{k}{4}, \frac{k}{3}\right) \) to the circle \( x^2 + y^2 + 8x - 6y - 24 = 0 \) is:

• A. \( 7 \)
• B. \( 1 \)
• C. \( 12 \)
• D. \( 24 \)

Hint:

The length of a tangent from an external point to a circle is given by: \[ L = \sqrt{h^2 + k^2 - r^2} \]

Answer 1

The Correct Option is B

Using the tangent length formula from a point \( (h, k) \) to a circle: \[ L = \sqrt{h^2 + k^2 - r^2} \] After substituting values and solving, we obtain: \[ L = 1 \]