Ellipse standard equation from graph

so we have an ellipse graphed right over here what we're going to try to do is find the equation for this ellipse so like always pause this video and see if you can figure it out on your own alright so let's just remind ourselves the form of an equation of ellipse so let's say our ellipse is centered at the point so I'm going to speak in generalities first and then we'll think about the specific numbers for this particular ellipse so say the center is at the point H comma K and let's say that you have a horizontal radius so the radius in the x-direction horizontal radius radius is equal to a and let's say you're a vertical radius let's say you're a vertical radius radius is equal to B then you're the equation of this ellipse is going to be is going to be X minus H X minus H squared over your horizontal radius squared so your radius in the X Direction squared plus plus now I'll think about what we're doing in the vertical direction Y minus the Y minus the y coordinate of our Center so Y minus K squared over the vertical radius squared B squared is equal to 1 is equal to 1 so what are H and K and a and B in this kit situation well H and K are pretty easy to figure out the center of this ellipse is at the point c the x-coordinate is negative 4 and the y-coordinate is 3 so this right over here is negative 4 and this right over here is positive 3 and what is a going to be well a is your horizontal radius your radius in the horizontal direction so it's the length of this line right over here and we can see it's 1 2 3 4 5 units long so a in this case is equal to five so this is going to be five squared and B is our radius of the vertical direction we can see it's one two three four units so B is equal to four so that is four so we can rewrite this as we could rewrite this is X minus negative four and we can simplify that in a second X minus negative four squared over five squared over our horizontal radius squared so it's going to be 25 plus y minus three squared y minus the y coordinate of our Center Y minus three squared over our vertical radius squared so B squared is going to be 16 and that is going to be equal to one and of course we could simplify this a little bit if I subtract a negative that's the same thing as adding a positive so I can get rid of I can just instead of saying X minus negative four I could just say X plus four and there you have it we have the equation for this ellipse