Question

How do you graph `(x-1)^2+(y-4)^2=9`?

Answer 1

You find the centre, the vertices, and the endpoints of the function. Then you plot the graph.

Explanation:

`(x-1)^2 + (y-4)^2 = 9`

This is the standard form for the equation of a circle with centre at (`1,4`) and radius `sqrt9 = 3`.

This means that, to find the vertices, you go 3 units up from the centre and 3 units down.

Thus, the vertices are at (`1,7`) and (`1,1`).

To find the endpoints, you go 3 units left of the centre and 3 to the right.

Thus, the endpoints are at (`-2,4`) and (`4,4`).

Plot these points on a graph.

Now draw a smooth circle through these four points.

And you have your graph.