Identifyng the conic?

Question

How do I identify the conic and write it in standard form?

Heres some examples:
x^2+4y^2=16
x^2+y^2-2x+4y+1=0
2x^2-4x+y+5=0

Answer 1

First one is a circle. You can see that the format fits the standard form of the circle, x^2 + y^2 = r^2.
x^2+4y^2=16
is a circle of center at origin, radius of 4

Second one, you have to complete the square first before you can identify it.

x^2+y^2-2x+4y+1=0
x^2-2x+1 + y^2+4y+4=-1+1+4
(x-1)^2 + (y+2)^2 = 4

This is a circle of center at (1, -2) radius of 2

You do the last one. Complete the square, then you'll notice, to bring it to the standard form, you'll have to deal with the coeffecient by dividing.