A circle is represented by the equation x^2 + 8x + y^2 - 12y = -29. Describe the algebraic techniques needed to rewrite the equation in standard form. Identify the center and radius of the circle. Show your work.

The simplest case is that of a circle whose centre is at the origin. Let us take an example. What

will be the equation centred on the origin with radius 5 units?

5

P(x, y)

x

y

5

5

−5

−5

O N

If we take any point P(x, y) on the circle, then OP = 5 is the radius of the circle. But OP is also

the hypotenuse of the right-angled triangle OPN, formed when we drop a perpendicular from P

to the x-axis. Now in the right-angled triangle, ON = x and NP = y. Thus, using the theorem

of Pythagoras,

x

2 + y

2 = 52 = 25 .

Step-by-step explanation:

step-by-step explanation: