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## Center and radii of an ellipse

Current time:0:00Total duration:1:40

# Ellipse graph from standard equation

## Video transcript

- [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. So 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. So 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. But 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. And 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.