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

1 Answer
Oct 28, 2015

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.

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