If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

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

whereas which ellipse is represented by the equation X minus 4 squared over 16 plus y minus 1 squared over 49 is equal to 1 and we're given a bunch of choices here we're given 4 choices here so let's just think about what's going on here so the center of the lips is going to be 4 comma 1 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 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 4 comma 1 so the center here is not 4 comma 1 the center over here is not 4 comma 1 not 4 comma 1 the only choice that has a Center at 4 comma 1 is this one over here so we already know this is this is the choice without even looking at the horizontal and the vertical radius but we can verify that this works out because a horizontal radius right over here notice it goes this orange line which represents can represent the horizontal radius it has a length of 4 and so the horizontal radius is 4 and so we see indeed that 16 is the horizontal radius squared this is 4 squared and if we look at the vertical radius here we see it has a length of 7 we're going from y equals 1 to y equals 8 has a length of 7 and we see in that equation that this indeed is 7 squared so that was pretty straightforward