how to solve; Xsq + ysq-4x=0
x^2 -4x + y^2 =0
x^2 -4x +4 + y^2 =4
(x-2)^2 + (y+0)^2=4
look like a circle to me.
To solve the equation x^2 + y^2 - 4x = 0, we can follow these steps:
Step 1: Rearrange the equation
First, rearrange the equation so that the x-terms are grouped together and the constant term is moved to the other side of the equation:
x^2 - 4x + y^2 = 0
Step 2: Complete the square
To complete the square, we want to rewrite the equation in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
To do this, first complete the square for the x-terms:
x^2 - 4x = (x^2 - 4x + 4) - 4 = (x - 2)^2 - 4
Now, the equation becomes:
(x - 2)^2 - 4 + y^2 = 0
Step 3: Simplify
Combine like terms:
(x - 2)^2 + y^2 = 4
Step 4: Interpret the equation
The equation (x - 2)^2 + y^2 = 4 represents a circle with center (2, 0) and radius 2. The term (x - 2)^2 represents the horizontal shift of the circle's center, while y^2 represents the vertical shift. The constant 4 represents the square of the radius.
Therefore, the original equation x^2 + y^2 - 4x = 0 represents a circle with center (2, 0) and radius 2.