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

1 Answer
Feb 6, 2015

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]}