Graphing Circles  Finding the radius
posted by Knights on .
A circle is tangent to the yaxis at the point (0,2) and passes through the point (8,0). Find the radius of the circle.
I tried using distance formula but it doesnt work? Help please thanks.

since the line y = 2 is tangent to the circle, its centre must lie on the yaxis
let the centre be (0,b)
the equation of the circle is
x^2+ (yb)^2 = r^2
but (0,2) lies on it > (2b)^2 = r^2
but (8,0) lies on it > 64 + (0b)^2 = r^2
64 +b^2= r^2
then 64 + b^2 = (2b)^2
64 + b^2 = 42b+b^2
60 = 2b
b = 30
the centre is (0, 30) > radius = 2(30) = 32
OR
distance from (0,b) to (0,2) must equal the distance from (0,2) to (8,0)
2b = √(64 + b^2)
square both sides
42b+b^2 = 64+b^2
2b = 60
b = 30
the radius is 2  (30) = 32