SOLUTION: A circle is centered at (2,1) and tangent to the line x+y=0. (a) find the equation of the circle (b) find the area and circumference of the circle.

Algebra ->  Circles -> SOLUTION: A circle is centered at (2,1) and tangent to the line x+y=0. (a) find the equation of the circle (b) find the area and circumference of the circle.      Log On


   

Question 1168232: A circle is centered at (2,1) and tangent to the line x+y=0.
(a) find the equation of the circle
(b) find the area and circumference of the circle.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A circle is centered at (2,1) and tangent to the line x%2By=0.

(a) find the equation of the circle
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2+............center at (2,1)
%28x-2%29%5E2%2B%28y-1%29%5E2=r%5E2
tangent to the line x%2By=0 =>y=-x => if the line is tangent to the given circle then we can find the equation of the line parallel to y=-x and passes through the center
y=mx%2Bb
m+-is same if lines are parallel
so, m=-1
y=-x%2Bb ......since passing through center(2,1)
1=-2%2Bb
b=1%2B2
b=3
so, the line parallel to tangent and passing through center is y=-x%2B3

distance between two parallel lines we can find radius


the equation of the circle
%28x-2%29%5E2%2B%28y-1%29%5E2=%283sqrt%282%29%2F2%29%5E2
%28x-2%29%5E2%2B%28y-1%29%5E2=4.5

(b) find the area and circumference of the circle.

radius=+3sqrt%282%29%2F2=2.12132
area enclosed
A=r%5E2%2Api
A=2.12132%5E2%2Api
A=14.1372
circumference
C=2r%2Api
C=2%2A2.12132%2Api
C=13.3286