Question

draw a circle with this equation. click circle icon, then on center, then on a point on the circle.\\(x^2 + 2x + y^2 - 4y = 4\\).

Explanation:

Step1: Group x and y terms

$x^2 + 2x + y^2 - 4y = 4$

Step2: Complete the square for x

$x^2 + 2x + 1 + y^2 - 4y = 4 + 1$

Step3: Complete the square for y

$x^2 + 2x + 1 + y^2 - 4y + 4 = 4 + 1 + 4$

Step4: Rewrite in standard circle form

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

Step5: Identify center and radius

Center: $(-1, 2)$, Radius: $\sqrt{9}=3$

Answer:

Center of the circle is $(-1, 2)$, and a point on the circle (e.g., $(2, 2)$, since moving 3 units right from the center lands on this point) can be used to draw the circle.