Length of tangent from (8, 6) to the circle ${ x }^{ 2 }+{ y }^{ 2 }-3x-4y+2=0$ is

Using the tangent length formula L = sqrt(x1^2 + y1^2 + 2gx1 + 2fy1 + c), we substitute the external point (8, 6) into the circle's equation x^2 + y^2 - 3x - 4y + 2 = 0. This yields L = sqrt(8^2 + 6^2 - 3(8) - 4(6) + 2). Evaluating the expression gives sqrt(64 + 36 - 24 - 24 + 2) = sqrt(54), which simplifies to 6 sqrt(2) units.

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