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What is the distance from a defined point on the x axis to the centre of circle x2 plus y2 -2x -6y plus 5 equals 0 when its tangent is at 3 4 on the Cartesian plane?
Wiki User
∙ 6y ago
Equation of circle: x^2 +y^2 -2x -6y +5 = 0
Completing the squares: (x-1)^2 +(y-3)^2 = 5
Center of circle: (1, 3)
Tangent contact point: (3, 4)
Slope of radius: ((3-4)/(1-3) = 1/2
Slope of tangent line: -2
Equation of tangent line: y-4 = -2(x-3) => y = -2x+10
Equation tangent rearranged: 2x+y = 10
When y equals 0 then x = 5 or (5, 0) as a coordinate
Distance from (5, 0) to (1, 3) = 5 using the distance formula
Wiki User
∙ 6y ago
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