 Krishna
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Step 1: Note down the equation and convert that equation into the standard form of the circle.

NOTE: Standard form (x - h)^2 + (y - k)^2 = r^2

Where center  (h, k) and radius r

Skill 1: Take down the equation and separate the similar variables.

EXAMPLE: x^2 + y^2 - 6x + 4y = 12

(x^2 - 6x) +(y^2 + 4y) = 12

Skill 2: According signs of the equation convert these as

either (a+b)^2 \text{ or } (a-b)^2.

Skill 3: Find out the a and b by convert the equation to

a^2 ± 2ab and compare.

EXAMPLE: [/math]x^2 - 6x[/math]

a = x

for b =?, take middle term - 6x = 2*3*x

And compare it with the 2ab

b = 3.

Skill 4: Substitute the values of a and b in the formulas of (a±b)^2.

NOTE: Use the formulas of   (a+b)^2 \text{ or } (a-b)^2

(a+b)^2 = a^2 + 2ab + b^2.

a^2+2ab=(a+b)^2-b^2.

or

a^2 - 2ab = (a-b)^2 - b^2 .

EXAMPLE:

$[(x-3)^2-9]+\left[\left(y+2\right)^2-4)\right]=12$

(x-3)^2+(y+2)^2=12+9+4

(x-3)^2+(y+2)^2=25

Step 2: Note down the given  circle equation

EXAMPLE: (x -2)^2 + (y + 1)^2 = \frac{169}{4}

Step 3: Compare the given equation with the Standard Form of circle equation.

EXAMPLE: $(x-2)^2+\left[y-\left(-1\right)\right]^2=\frac{169}{4}$ Compare it with

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

Where center  (h, k) and radius r

Step 4: Identify the r, h and k values.