Question

How do I graph the ellipse with the equation `(x−4)^2/36+(y-3)^2/36=1`?

Answer 1

First of all... this is not an ellipse, o better... this is a very particular ellipse. This is a circle!

An ellipse have an equation like this:

`(x-x_c)^2/a^2+ (y-y_c)^2/b^2=1`, where `C(x_c,y_c)` is the center, `a` is the orizontal semi-axis and `b` is the vertical semi-axis.

But... if `a=b`, the semi-axes are equal and so it is a circle.

In our case:

`(x-4)^2/36+(y-3)^2/36=1rArr(x-4)^2+(y-3)^2=36` is the equation of a circle with centre `C(4,3)` and radius `6`, and thisis its graph:

graph{(x-4)^2+(y-3)^2=36 [-20, 20, -10, 10]}