# How do you find the center of the circle with equation #(x - 3)^ 2 + (y + 4)^ 2 = 25#?

##### 2 Answers

#### Explanation:

the standard eqn of a circle with centre

is

so for

comparing this with

the centre will be

for good measure the radius will be

Centre

#### Explanation:

Note that the equation of a circle centred at the origin is derived using Pythagoras. This is because you can form a triangle related to any point on the perimeter.

The behaviour of the question's equation is such that it models the following:

Draw the circle at the origin where

Move every point that is at

Move every point that is at

The net effect is that you move the plot to the right by 3 and down by 4. This puts the new centre at

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Consider the

This is in fact:

So

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Consider the

This is in fact:

So

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