Question

Write each equation in standard form. Identify the important features of the graph.
x^2 + y^2 - 8x + 10y + 15 = 0
y^2 + 4y - 8x + 4 = 0

Answer 1

{x^2-8x+(-8/2)^2-(-8/2)^2}+{y^2+10y+(10/2)^2-(10/2)^2}+15=0
(x-4)^2-16+(y+5)^2-25+15=0
(x-4)^2+(y+5)^2=(sqrt26)^2
it is a circle with centre (4,-5) and radius=sqrt26

Answer 2

y^2+4y+4=8x
(y+2)^2=8x
it is a parabola with vertex (0,-2)