Posted by Knights on Sunday, March 10, 2013 at 8:32am.
A circle is tangent to the y-axis 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.
- Graphing Circles - Finding the radius - Reiny, Sunday, March 10, 2013 at 9:33am
since the line y = 2 is tangent to the circle, its centre must lie on the y-axis
let the centre be (0,b)
the equation of the circle is
x^2+ (y-b)^2 = r^2
but (0,2) lies on it ----> (2-b)^2 = r^2
but (8,0) lies on it ----> 64 + (0-b)^2 = r^2
64 +b^2= r^2
then 64 + b^2 = (2-b)^2
64 + b^2 = 4-2b+b^2
60 = -2b
b = -30
the centre is (0, -30) ---> radius = 2-(-30) = 32
distance from (0,b) to (0,2) must equal the distance from (0,2) to (8,0)
2-b = √(64 + b^2)
square both sides
4-2b+b^2 = 64+b^2
-2b = 60
b = -30
the radius is 2 - (-30) = 32
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