how can i sketch x^2+y^216x+8y+16=0
can you give me please try to explain the steps that i need to do
thanks
this is a circle that needs to be put in standard form to easily sketch it. I was able to realize that since the coefficients of the $\displaystyle x^2$ and $\displaystyle y^2$ are the same, namely =1
We must complete the square for both x and y, so we divide the coefficient of the x and y terms by 2, square them, and add them to both sides
$\displaystyle x^2+y^216x+8y+16=x^216x+(8)^2+y^2+8y+4^2+16=8^2+4^2$
And now we can factor
$\displaystyle (x8)^2+(y+4)^2=64+1616=64$
Can you sketch that now or do you need further assistance?
(x  8)^2 + (y + 4)^2 = 64 = 8^2
compare it with the standard equation of a circle, that is
(x  h)^2 + (y + 4)^2 = r^2,
h,k is the CORDINATE of the center of the CIRCLE, where r is the radius.
from (x  8)^2 + (y + 4)^2 = 64 = 8^2; center coordinate is (h,k) is (8,4) and r = 8.
see the graph . . . .
if the standard equation of the circle awe you, resort to point plotting, maybe you have not encounter yet ANALYTIC GEOMETRY.
