Graph the ellipse and locate the foci. (y^2)/25 + (x^2)/16 = 1

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Hello. Today we're going to be using the given equation to graph the shape of the lips. So what we are given is y squared over plus X squared Over 25 is equal to one. Now, the standard form of an ellipse always has the X term first. So by quickly rewriting this, we can rewrite this equation to give us X squared over 25 plus Y squared over 64 is equal to one. So this is the standard form of an ellipse whose center is at the origin. But keep in mind that the denominator of the Y term is greater than the denominator of the X term. That means that this standard form of the ellipse is of the form X squared over B squared plus Y squared over a squared is equal to one. And this is the shape of an ellipse whose major axis is the Y axis. So we're going to have a vertical ellipse. So now that we know that the major axis is the Y axis, let's go ahead and identify the vertex is for the major and minor axis, the vortices for the major axis is going to be denoted by the a variable. And here we have a squared is equal to 60. For by taking the square root of both sides of this equation, we get A is equal to plus or minus eight. And again, since the major axis is the Y axis, that means that these vortices are going to be located at zero comma eight and zero comma negative eight. Now let's go ahead and identify the vertex is for the minor axis which is denoted by the B variable. Here we have, B squared is equal to 25. If we take the square root of both sides we get B is equal to plus or minus five since the major axis is the y axis. That means the minor axis is the X axis. So that means that these vortices are going to be located at five comma zero and negative five comma zero. Now we need to identify the location of the fosse. The equation of the faux sign is given to us as C is equal to the square root of a squared minus b squared. And we know that a squared is equal to 64 b squared is equal to 25. So if we plug in the respective values we get the square root of 64 minus 25 this is going to simplify to the square root of 39. The square root of 39 cannot be simplified any further. So we're going to leave it as plus or minus the square root of 39. Now keep in mind that the fosse is located on the major axis and the major axis is the y axis in this case. So that means that the locations of the fosse are going to be at zero comma square root of 39 and zero comma negative square root of 39. So now that we have all the information we need, we just need to select the correct graph for the ellipse and that graph is going to be option A. C. Here we are told that the fosse is at zero comma negative square root 0 comma square root 39 which matches what we found here. We also have the major axis which has vertex is at zero comma eight and zero comma negative eight. And the minor versaces are going to be at 5:00 and -5:00. And the origin Is going to be at 0:00. So with all that being said, the answer to this problem is going to be a So I hope this video helps you in understanding how to graph in the lips and I'll go ahead and see you all in the next video.

Graph the ellipse and locate the foci. (y^2)/25 + (x^2)/16 = 1

Key Concepts

Ellipse Definition

Foci of an Ellipse

Graphing an Ellipse

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