Ellipse graph from standard equation

0:00- [Voiceover] We're asked which ellipse is represented by the equation x minus four squared over 16 plus y minus one squared over 49 is equal to one. And we're given a bunch of choices here. We're given four choices here. So let's just think about what's going on here.

0:13So the center of the ellipse is going to be four comma one. How do I know that? Well the equation of the ellipse is going to be x minus the x-coordinate for the center squared over here, over the horizontal axis is horizontal radius squared plus y minus the y-coordinate of the center squared over the vertical radius squared.

0:36So the center is going to be four comma one. So the center here is not four comma one. The center over here is not four comma one. Not four comma one. The only choice that has a center at four comma one is this one over here. So we already know this is the choice without even looking at the horizontal and the vertical radius.

0:59But we can verify that this works out 'cause a horizontal radius right over here, notice it goes this orange line, which can represent the horizontal radius. It has a length of four and so the horizontal radius is four and so we see indeed that 16 is the horizontal radius squared, this is four squared.

1:21And if we look at the vertical radius here, we see it has a length of seven. We're going from y equals one to y equals eight, has a length of seven. And we see in that equation that this indeed is seven squared. So that was pretty straight forward.