SOLUTION: Write the equation of a circle that has the center on the x-axis, a radius of 1, and passes through the point (((square root of 2)/2),((square root of 2)/2)).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of a circle that has the center on the x-axis, a radius of 1, and passes through the point (((square root of 2)/2),((square root of 2)/2)).      Log On


   

Question 636108: Write the equation of a circle that has the center on the x-axis, a radius of 1, and passes through the point (((square root of 2)/2),((square root of 2)/2)).
Found 2 solutions by ewatrrr, lwsshak3:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Write the equation of a circle that has the center on the x-axis, 

a radius of 1, and passes through the point 

(+%28sqrt%28+2%29%2F2%29+,%28sqrt%282%29%2F2%29)

  (x,0)

 D = sqrt%28%28sqrt%28+2%29%2F2+-x+%29%5E2+%2B+2%2F4%29%29 = 1  , sqrt%28+2%29%2F2%29 -x  =± 1%2Fsqrt%282%29+=+sqrt%282%29%2F2 , x = sqrt%282%29

  

%28x-sqrt%282%29%29%5E2+%2B+y%5E2+=+1%5E2

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of a circle that has the center on the x-axis, a radius of 1, and passes through the point (((square root of 2)/2),((square root of 2)/2)).
**
Equation of a circle: %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2, (h,k)=(x,y) coordinates of center, r=radius
For given circle:
r^2=1
r=1
k==0
equation:
(x-h)^2+y^2=1
solve for h using coordinates of given point (√2/2, √2/2)
(√2/2-h)^2+(√2/2)^2=1
2/4-√2h+h^2+2/4=1
h^2-√2h+1=1
h^2-√2h=0
h(h-√2)=0
h=0 (reject, does not check)
h=√2
Equation: (x-√2)^2+y^2=1