# How do you decide whether or not the equation below has a circle as its graph If it does, give the center and the radius. If it does not, describe the graph #25x^2 +25y^2- 30x+ 30y -18 =0#?

##### 2 Answers

The eqn. represents a circle having centre

#### Explanation:

The **General Second Degree Equation** in

**Circle** , if,

In the event, its **Centre** is **Radius** is

In our Example,

So, the eqn. represents a circle having centre #(15/25,-15/25), i.e.,

Enjoy Maths.!

Yes it is an equation of a circle.

#### Explanation:

Given:

If this an equation of a circle then we should be able to manipulate it back into standard form of

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I spot that the standard form is part of the process for completing the square. Lets investigate that.

Divide throughout by 25 to get rid of the coefficients for

Write as:

Completing the squares

Thus the centre as at point 1

The radius is

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Is the same as:

Thus it is a circle.