SOLUTION: Write the equation of the circle in standard form find the center, radius, intercepts and graph the circle x^2+y^2+10x+8y+16=0
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Question 671931: Write the equation of the circle in standard form find the center, radius, intercepts and graph the circle x^2+y^2+10x+8y+16=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 x^2+y^2+10x+8y+16=0
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Standard form of equation for a circle: , (h,k)=(x,y) coordinates of center, r=radius
For given equation:
x^2+y^2+10x+8y+16=0
complete the square.
(x^2+10x+25)+(y^2+8y+16)=-16+25+16
equation of circle: (x+5)^2+(y+4)^2=25
center:(-5,-4)
radius=√25=5
..
x-intercepts:
set y=0
x^2+10x+16=0
(x+8)(x+2)=0
x=-8
and
x=-2
..
y-intercepts
set x=0
y^2+8y+16=0
(y+4)^2=0
y=-4
see graph below:
y=(25-(x+5)^2)^.5-4
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