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sketch the graph of the given ellipse, labeling all intercepts.$$\begin{aligned}&9 x^{2}+4 y^{2}=36\\&4 x^{2}+9 y^{2}=36\end{aligned}$$

Graph is the answer

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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sketch the graph of the gi…

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Graph each ellipse.$$9…

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graph each ellipse.$$9…

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Graph each ellipse.$4 …

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Graph each ellipse.. $…

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Sketch the graph of each e…

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Graph each ellipse.$$<…

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Graph each ellipse. $9…

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graph each ellipse.$$3…

for this problem, we have been given the equation of an ellipse that we need to graph. So when we have an ellipse, it's important that we put it into standard form. That gives us all the information we need to graph it. So let's review standard form for an ellipse standard form for an Ellipse is gonna be two fractions and I'm going to do the denominator The denominators of second I'm gonna just the numerator is for a moment. So my numerator r x minus h squared plus y minus k squared and we always said it equal toe one. Now those numerator should look familiar. They're very, very similar to the standard form of a circle. And just like a circle, the center of my lips will be at the point. H k. Okay. My denominators. Tell me the orientation of my lips. We always use a to show the biggest number. So if the biggest number of a squared is under the X term, then that means that X is my major axis. And my, uh, lips is going to be ah, horizontal lips is gonna be that major axis will be horizontal on the X axis. If I switch these denominators and I put the bigger number A under the Y term, Well, then that means why is my major axis and I'm gonna have a vertical ellipse? So knowing where the biggest denominator is shows me the orientation of my lips. Now, let's take a look at the equation we've been given. One big difference is standard form. We always said it equal toe one, and this is set equal to 36. So what we're going to do is we're going to divide every term by 36 so that it can equal one. And when I simplify these, this gives me X squared over four plus y squared over nine. So that's in standard form. So let's see what this tells me. First we look at our numerator. I'm not subtracting anything from X and y, which means that both h and K R. Zero so the center of my lips is going to be the origin 00 What about our denominators? While our largest denominator is under the Y axis, So the Y axis is our major axis, and a is the square root of nine or three. So the Vergis ease for My lips are going to be three units away from the center along my y axis. So that's the 0.3 and zero negative three. Well, how fat or skinny is my lips? What do I do on the minor axis? Well defined, that we look at the other denominator that gives us B squared of forests, too, so I'll be going two units on either side on the minor axis. So that gives me 20 and negative 20 And to make my lips, I'm just going to connect those points. Make it nice and smooth of a curve as I can. So there's my lips. That ellipse is the graph of Are Given Equation nine X squared plus four y squared equals 36.

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