Homework Help: analytic geometry helps are appreciated

Posted by Knights on Friday, March 1, 2013 at 9:14am.

For some positive real number r , the line x+y=r is tangent to the circle x^2+y^2 = r. Find r.

How do we do this? Set equal equations together??

analytic geometry helps are appreciated - drwls, Friday, March 1, 2013 at 10:23am
r^1/2 is the radius of the circle.
r is the y-intercept of the line
y = r - x.
It is tangent to the circle if
r^2 = 2*(sqrtr)^2
(from Pythagorean rule)
Therefore r^2 = 2r
r = 2

Plot the two functions
y = 2-x and
x^2 + y^2 = 2
You will see that there is tangency at
(sqrt2, sqrt2)
analytic geometry helps are appreciated - Knights, Friday, March 1, 2013 at 10:38am
thanks a bunch sire

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