x2+y2-2x+4y-4=0

Add 4 to both sides of the equation.

x2+y2-2x+4y=4

Use the form ax2+bx+c, to find the values of a, b, and c.

a=1,b=-2,c=0

Consider the vertex form of a parabola.

a(x+d)2+e

Substitute the values of a and b into the formula d=b2a.

d=-22(1)

Simplify the right side.

Cancel the common factor of 2.

Cancel the common factor.

d=-22⋅1

Divide 1 by 1.

d=-1⋅1

d=-1⋅1

Multiply -1 by 1.

d=-1

d=-1

Find the value of e using the formula e=c-b24a.

Simplify each term.

Raise -2 to the power of 2.

e=0-44⋅1

Multiply 4 by 1.

e=0-44

Divide 4 by 4.

e=0-1⋅1

Multiply -1 by 1.

e=0-1

e=0-1

Subtract 1 from 0.

e=-1

e=-1

Substitute the values of a, d, and e into the vertex form a(x+d)2+e.

(x-1)2-1

(x-1)2-1

Substitute (x-1)2-1 for x2-2x in the equation x2+y2-2x+4y=4.

(x-1)2-1+y2+4y=4

Move -1 to the right side of the equation by adding 1 to both sides.

(x-1)2+y2+4y=4+1

Use the form ax2+bx+c, to find the values of a, b, and c.

a=1,b=4,c=0

Consider the vertex form of a parabola.

a(x+d)2+e

Substitute the values of a and b into the formula d=b2a.

d=42(1)

Cancel the common factor of 4 and 2.

Factor 2 out of 4.

d=2⋅22⋅1

Cancel the common factors.

Factor 2 out of 2⋅1.

d=2⋅22(1)

Cancel the common factor.

d=2⋅22⋅1

Rewrite the expression.

d=21

Divide 2 by 1.

d=2

d=2

d=2

Find the value of e using the formula e=c-b24a.

Simplify each term.

Cancel the common factor of (4)2 and 4.

Factor 4 out of (4)2.

e=0-4⋅44(1)

Cancel the common factors.

Cancel the common factor.

e=0-4⋅44⋅1

Rewrite the expression.

e=0-41

Divide 4 by 1.

e=0-1⋅4

e=0-1⋅4

e=0-1⋅4

Multiply -1 by 4.

e=0-4

e=0-4

Subtract 4 from 0.

e=-4

e=-4

Substitute the values of a, d, and e into the vertex form a(x+d)2+e.

(y+2)2-4

(y+2)2-4

Substitute (y+2)2-4 for y2+4y in the equation x2+y2-2x+4y=4.

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

Move -4 to the right side of the equation by adding 4 to both sides.

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

Add 4 and 1.

(x-1)2+(y+2)2=5+4

Add 5 and 4.

(x-1)2+(y+2)2=9

(x-1)2+(y+2)2=9

This is the form of a circle. Use this form to determine the center and radius of the circle.

(x-h)2+(y-k)2=r2

Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

r=3

h=1

k=-2

The center of the circle is found at (h,k).

Center: (1,-2)

These values represent the important values for graphing and analyzing a circle.

Center: (1,-2)

Radius: 3

Graph x^2+y^2-2x+4y-4=0