Question 789558: Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle.
x^2+y^2−10x−4y+13=0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle.
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Sandard form of equation for a circle: (x-h)^2+(y-k)^2=r^2, (h,k)=(x,y) coorinates of the center, r=radius
x^2+y^2−10x−4y+13=0
x^2−10x+y^2−4y+13=0
complete the square:
(x^2−10x+25)+(y^2−4y+4)=-13+25+4
(x-5)^2+(y-2)^2=16
center:(5,2)
radius=√16=4
..
x-intercepts:
set y=0
x^2-10x+13=0
solve for x by quadratic formula:
a=1, b=-10, c=13
ans:
x≈1.5359
or
x≈8.4641
..
y-intercepts:
set x=0
y^2-4y+13=0
a=1, b=-4, c=13
discriminant=b^2-4ac=16-4*1*13=16-42<0
y-intercepts: none
See graph below:
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