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Sketch the graph of $\frac{(x-1)^{2}}{4}+\frac{(y+2)^{2}}{9}=1$

Graph is the answer

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Campbell University

Oregon State University

McMaster University

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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04:47

Sketch the graph$\frac…

05:52

01:28

Sketch the graph of each e…

0:00

Graph.$$\frac{(x+2…

01:32

04:43

Graph the following equati…

01:00

01:38

Graph: $9 x^{2}+4 y^{2}=1$…

00:38

Plot the graph of the give…

01:03

Sketch a graph of $(x-2)^{…

01:30

Graph $(x-2)^{2}+(y+1)^{2}…

01:19

01:52

Sketch the graph.$$-x^…

00:49

Sketch the graph.$$x^{…

for this problem. We have been given the equation of an ellipse, and our goal is to graph that equation. Well, in order to do that, let's take a step back and review the standard form of an ellipse. So we understand what all these numbers mean when we go to graph hm, an ellipse. The standard form is going to be as two fractions right now. I'm going to write the numerator. I'm gonna come back to the denominators in a moment. My enumerators are X minus H squared. Plus why minus k squared. And we always said it equal toe one That numerator pair should look very similar is quite similar to the standard form of a circle. And just like a circle, the center of the Ellipse will be at the point HK. So let's take a look at the equation. We've been given what our H and K. Well, it's X minus one. So h is one is why plus two, which is the same, is why minus negative, too. So that's the center of my lips. The 0.1 negative too. So I'm gonna just graph that in there so we don't lose it now. Let's go back and look at those denominators We always call the largest denominator a squared. So if a square is that biggest denominator is under the X term. That means X is my major axis and I have ah, horizontal ellipse. But if I switch these denominators, if I put the biggest one under the why term Well, now why is my major axis and I have a vertical ellipse? So where that largest denominator is identifies the orientation of my lips. So let's go back and look at the equation we've been given. Our biggest denominator is nine, and that's under the Y term. So the Y axis is my major axis and A is three. So I'm going to start at the center, which I've already graft. I'm gonna go along up and down, parallel to the Y axis. I'm going to go up three points and down three. Those are the vergis ease of my ellipse. Those of the endpoints of my major axis To find the width of my lips. I look to the minor axis that gives me be in this case, B is too. So I'm going to start at the center of my lips, and I'm going to go on the minor axis in this case, parallel to the X two units in either direction. And now I'm going to connect these dots. So that is a sketch of the Ellipse with the given equation.

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