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

The answer is 4.Step-by-step explanation:I m taking the test TwT...

Identify the standard form of a circle equation

alexkrol30083

11.01.2022

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

0,0(0 оценок)