What is the length of the tangent line from the point 8 2 to a point where it meets the circle x2 plus y2 -4x -8y -5 equals 0?

What is the length of the tangent line from the point 8 2 to a point where it meets the circle x2 plus y2 -4x -8y -5 equals 0?
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Answer :

Equation of circle: x^2 +y^2 -4x -8y -5 = 0Completing the squares: (x-2)^2 +(y-4)^2 = 25 which is radiussquaredCenter of circle: (2, 4)Tangent line originates from: (8, 2)Distance from (8, 2) to (2, 4) is sq rt of 40 which ishypotenuse of right angle triangleUsing Pythagoras theorem: distance^2 minus radius^2 = 15Therefore length of tangent line is the square root of 15
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