# How do you graph (x-2)^2 + (y+5)^2?

Oct 28, 2015

Transposed circle.

#### Explanation:

This is the equation of a circle so you should really have stated it as: ${\left(x - 2\right)}^{2} + {\left(y + 5\right)}^{2} = {r}^{2}$

This equation is derived from Pythagoras relating the sides of a triangle where ${\left(\text{hypotenuse")^2 = ("opposite")^2 + ("adjacent}\right)}^{2}$

Changing the values of x and y by constant values means that you have moved the centre of the circle away from the origin. The origin being $\left(x , y\right) \to \left(0 , 0\right)$

So the centre has moved to -2 on the x-axis and to +5 on the y axis.

To actually draw the graph you need to know the value of the radius $r$. If $r$ is not given then make one up that is easy to use.

Circle at the origin. Move every point to $\left(x - 2 , y + 5\right)$
So put the needle of your compass at $\left(- 2 , 5\right)$ and draw your circle.