Question 48281
x^2 + y^2 + 2x - 2y = 2
x^2 + 2x + y^2 - 2y = 2
(x + 1)^2 + (y - 1)^2 = 2 + 1 + 1 = 4
(x + 1)^2 + (y - 1)^2 = 4
Circle with radius of 2 units and center at (-1,1).
{{{graph(600,600,-10,10,-10,10,sqrt(4 - (x + 1)^2)+1,-sqrt(4 - (x + 1)^2)+1)}}}
x-intercepts:
x^2 + 2x + y^2 - 2y = 2
x^2 + 2x + 0^2 - 2(0) = 2
x^2 + 2x - 2 = 0
{{{x = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}}
{{{x = (-2 +- sqrt( 4 + 8 ))/(2) }}}
{{{x = (-2 +- 2*sqrt( 3 ))/(2) }}}
{{{x = -1 +- sqrt(3) }}}
P({{{ -1 + sqrt(3) }}},0) and P({{{ -1 - sqrt(3) }}},0)
y-intercept:
x^2 + 2x + y^2 - 2y = 2
0^2 + 2(0) + y^2 - 2y = 2
y^2 - 2y - 2 = 0
{{{x = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}}
{{{x = (2 +- sqrt( 4 + 8 ))/(2) }}}
{{{x = (2 +- 2*sqrt( 3 ))/(2) }}}
{{{x = 1 +- sqrt( 3 ) }}}
P(0,{{{ 1 + sqrt(3) }}}) and P(0,{{{ 1 - sqrt(3) }}})