Circle
Length of Tangent
Premium Question
Grade 11
Question:
The length of the tangent from the point $(5, 1)$ to the circle $x^2 + y^2 + 6x - 4y - 3 = 0$ is:
(1) $81$
(2) $9$
(3) $7$
(4) $\sqrt{5}$
Step-by-Step Solution
Key Concept: Length of tangent $= \sqrt{S_1}$ where $S_1 = 5^2 + 1^2 + 6(5) - 4(1) - 3 = 25 + 1 + 30 - 4 - 3 = 49$. Hence length $= 7$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)