Find the radius r of the circle which has center (5,0) and is tangent to the line y = 2x.

Mathematics
Tutor: None Selected Time limit: 1 Day

Find the radius r of the circle which has center (5,0) and is tangent to the line y = 2x.

Jun 1st, 2015

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Jun 1st, 2015

Is the point of tangency given in the question?

Jun 1st, 2015

no the point of tangency is not given

Jun 1st, 2015

no the point of tangency is not given

Jun 1st, 2015

no the point of tangency is not given

Jun 1st, 2015

Given the tangent line y =2x

So slope of the line perpendicular to the tangent line containing the radius (5,0) will be

-1/2

so the equation of the perpendicular line is y -0 = -1/2 (x-5)

                                                                    y = -1/2 (x-5)

To find the point of tangency, equate y = 2x to y = -1/2 (x-5)

                              so 2x = -1/2 (x-5)

                                    -4x = x-5

                                     -5x= -5

                                       x=1

                                so y =1*2 = 2

so the point of tangency = (1,2)

so radius^2 = (1-5)^2+ (2-0)^2

                    = 16 +4 =20

so radius r = sqrt(20) = 2 sqrt(5)

Please let me know if you have any questions and best me if you are satisfactory.

Jun 1st, 2015

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