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What are the lengths of the tangent lines from the origin to the circle x squared plus y squared -6y plus 4x plus 10 equals 0 on the coordinated grid?
Wiki User
∙ 7y ago
Tangents stem from the origin: (0, 0)
Circle equation: x^2 +y^2 -6x +4y +10 = 0
Completing the squares: (x+2)^2 +(y-3)^2 -4 -9 +10 = 0
So: (x+2)^2 +(y-3)^2 = 3 which is the radius squared
Centre of circle: (-2, 3)
Distance from (-2, 3) to (0, 0) = 13 which is distance squared
Lengths of tangents using Pythagoras: 13-3 = 10 => square root of 10
Take note that the distance from (-2, 3) to (0, 0) is actually the hypotenuse of a right angle triangle.
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoThey are of length 10.
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