finding points of intersection?

Question

http://college.hmco.com/mathematics/larson/algebra_trig/7e/assets/students/cp/03.pdf

How do you get from the original eqation of:

X^2+Y^2-3X+5Y-11=0 all the way to the solution (which they give as the top and botom half of the circle)??? Please help, THANK YOU

Answer 1

They solved for y. Use quadratic formula on

y² + 5y + (x² - 3x - 11) = 0

y = [-5 ± sqrt(5² - 4(x² - 3x - 11))]/2
= [-5 ± sqrt(25 - 4x² + 12x + 44)]/2
= ½ (-5 ± sqrt(69 - 4x² + 12x))

So
y = ½ (-5 + sqrt(69 - 4x² + 12x)) or
y = ½ (-5 - sqrt(69 - 4x² + 12x))

which gives, respectively, the top half and the bottom half of the circle.