# How do you write the standard from of the equation of the circle given center:(2,-6) radius: 2?

##### 1 Answer

See explanation as to why it is in this form.

#### Explanation:

The standardised formula for a circle with its centre at the origin is:

This is derived from Pythagoras rule about a 'right triangle'. You know the one;

However, in this case the centre is not at the origin. It is at

Consequently we mathematically move all the points as if the centre of the circle was at the origin so that

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

so each generic point we have

so each generic point we have

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Becomes: