The equation of a given circle in. general form is x^2+y^2+12y+27=0. write the equation in standard form, (x-h)^2+(y-k)^2=r^2, by completing the squares in the equation. show your work in the table.

Center (h, k) = (0, 6)

Radius, r = 3 units

Step-by-step explanation:

The given equation of the circle is:

STEP I: Move the constant term to the right hand side.

To do that we subtract 27 on both the sides, we get:

STEP II: Divide the co - effecient of 'x' by 2 and square it.

Here there is no 'x' term. Its co-effecient is 0.

STEP III: Add the result on both sides.

Since, we got 0 in the previous step, there would no change in the equation

STEP IV: We repeat the process for 'y'.

Here, the co-effecient of 'y' is: 12.

Dividing by 2 and squaring it will yield:

STEP V: Adding 36 to both the sides of the equation, it becomes:

We have arrived at perfect squares.

STEP VI: Write in the form of perfect squares.

STEP VII: Compare it with the standard form.

We get: The centre of the circle: (h, k) = (0, 6) and

the radius of the circle, r = 3 units.

75

step-by-step explanation:

e

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)