Question

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

Answer 1

Transposed circle.

Explanation:

This is the equation of a circle so you should really have stated it as: `(x-2)^2 +(y+5)^2 = r^2`

This equation is derived from Pythagoras relating the sides of a triangle where `("hypotenuse")^2 = ("opposite")^2 + ("adjacent")^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 `( x , y ) -> (0,0)`

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 `(x-2, y+5)`
So put the needle of your compass at `(-2,5)` and draw your circle.