What value of C is the line tangent to the circle
Geometry
Level
pending
For what values of C is the line Y = 4X + C tangent to the circle X^2 + Y^2 = 25.
20.01333456, 20.61552812
20.61552812, -20.61552812
The line does not intersect the circle or even touch the circle
20.01552812, -20.61552812
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1 solution
Equation of a straight line y = 4x + c
Substituting for Y in the equation X^2 + Y^2 = 25, we get
16x x + c c + 8xc + x*x = 25
17 x x+ 8 x c + c*c - 25 = 0
64 c c = 68 (c c -25)
4 c c = 68 * 25
c c = 17 25 c = +/- sqrt(17) * 5 or = +/- 20.61552812.