Question

Identify the standard form of a circle equation x^2+2x+y^2-2y=2

Answer 1

Answer:

The standard from of the expression is: $(x +1)^2 + (y-1)^2 = (2)^2$

Step-by-step explanation:

Here the given expression is :

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

Now, the standard form of a circle is given as :

$(x-h)^2 + (y -k)^2 = r^2$

Here, (h,k)  = Coordinates of Center,   r = Radius

Also, use the algebraic identity:

$(a \pm b)^2 = a^2 + b^2 \pm 2ab$

Now, converting the given expression in the standard form, we get:

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

Add 2 on both sides of the equation, we get:

$x^2+2x+y^2-2y +2=2 + 2\\\implies x^2+2x + 1 + y^2-2y + 1 = 4\\\implies (x^2+2x + 1 )+ (y^2-2y + 1) = 4\\\implies (x +1)^2 + (y-1)^2 = (2)^2$

So, here the standard from of the expression is:

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

Center coordinates here are  (h,k)  = ( -1 ,1) and Radius  = 2 units