The length of tangent from $(3,4)$ to circle $x^2+y^2=9$ is
- $4$
- $5$
- $ 6$
- $none\ of\ these$
Reveal answer
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A
Correct answer
Explanation
The length of the tangent from a point (x1, y1) to a circle x^2 + y^2 = r^2 is sqrt(x1^2 + y1^2 - r^2). Here, sqrt(3^2 + 4^2 - 3^2) = sqrt(9 + 16 - 9) = sqrt(16) = 4.
AI explanation
Apply the standard tangent length formula, which requires finding the square root of the difference between the square of the point's distance from the origin and the square of the circle's radius. The square of the distance from (3, 4) to the origin is 3^2 + 4^2, which equals 25. The circle x^2 + y^2 = 9 has a radius of 3, so its square is 9. The length of the tangent is the square root of (25 - 9), resulting in 4.