Question 392026
Find the center and length of radius of the circle:
Get the equation into standard form for a circle: {{{(x-h)^2+(y-k)^2 = r^2}}}
{{{x^2+y^2+20x-16y+80 = 0}}} Group the terms:
{{{(x^2+20x)+(y^2-16y)+80 = 0}}} Subtract 80 from both sides.
{{{(x^2+20x)+(y^2-16y) = -80}}}} Complete the square in x and y.
{{{(x^2+20x+100)+(y^2-16y+64) = 100+64-80}}} Simplify.
{{{(x+10)^2 + (y-8)^2 = 84}}} Compare with standard form above:
{{{h = -10}}}, {{{k = 8}}} , {{{r = sqrt(84)}}}
The coordinates of the center: (-10, 8)
Length of radius: {{{sqrt(84)}}} = {{{9.165}}}approx.