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

Graph is the answer

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Missouri State University

Harvey Mudd College

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).

03:18

sketch the graph of the gi…

02:41

02:46

00:50

Graph each ellipse.$4 …

03:54

Sketch the graph of each e…

02:16

Graph each ellipse.$$9…

01:39

graph each ellipse.$$9…

03:12

03:07

Graph each ellipse.. $…

02:26

02:57

01:21

02:38

02:53

Graph each ellipse.$$<…

01:44

Graph each ellipse. $9…

02:22

Sketch a graph of the elli…

02:02

Graph each ellipse.$x^…

01:48

03:30

graph each ellipse.$$3…

for this problem, we have been given the equation of an ellipse for X squared plus nine y squared equals 36 our goal is to graph the Ellipse. Now, to do this, we need to put our lips into standard form. Standard form shows us all the information we need to grab the Ellipse. So let's take a step back and review what the standard form for an ellipse looks like. Okay, I'm going to start its two fractions that we add together. I'm going to start with enumerators First the numerator czar x minus h squared. Plus why minus k squared. And we always said it equal toe one. Now those numerator should look familiar. They're very similar to the equation for a circle. And just like a circle HK shows us where the center of our lips is. And again, we're always going to set to some of these fractions equal toe one Now for the denominators, the bigger number we always call a. So if a the bigger number is under the X axis, that means the X axis is my major axis and I have ah, horizontal ellipse. But what if they're reversed? What if the a term that biggest term is under the why fraction under under my wife squared. Well, in that case, why is my major axis and I have a vertical the lips. So determining which denominator is the biggest one shows me the orientation of my lips and it tells me by A and my B. So let's take a look at the equation that we've been given. One big difference between standard form and the equation that we have is the fact that our equation does not equal one. So we need to start there. I'm going to divide every turn by 36 in order to set this equal toe one. And when I do so, that gives me X squared over nine plus why squared over four equals one. So this is standard form. So let's see what this tells us. First. Let's look at our numerator. I am not subtracting anything from either X or Y, which means both h and K R zero. So the center of this ellipse is at the origin 00 My biggest denominator is under the X axis. So the X axis is my major axis. I have ah horizontal ellipse, and I know that A is three is the square root of nine. So I'm going to start it to center. I'm going to go along my major access three units in either direction. That gives me the 0.30 and the point Negative 30 Those are the vergis ease of my lips. But what about the other direction? How do I know how fat or skinny my ellipses Well, to determine that we look at the other denominator and that tells us that B is too so again, starting at the center, I'm going to go on the minor axis in this case, the Y axis two units in either direction, which is the 0.2 and the 0.0 negative, too. I am just going to connect these four points so that is thick way Asian. Or that is the graph that matches the equation for the Ellipse that we were given for this problem.

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