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Sketch the graph of $\frac{(x+4)^{2}}{16}+\frac{(y-3)^{2}}{4}=1$

Graph is the answer

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

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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Sketch the graph of the gi…

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Sketch the graph of each e…

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$$\text {Sketch the graph …

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Sketch the graph of $y=4 x…

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Sketch the graph of the eq…

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Sketch the graph of the fu…

for this problem. We have been given the equation of an ellipse, and our goal is to sketch it now. In order to do that, let's take a step back and review the standard form of of an Ellipse. So we understand what all these numbers are when it comes time to sketch things on our grid. Standard form for an ellipse is two fractions added together Thio equal one now going to come back to my denominators in a moment. But here are my numerator X minus H squared plus y minus K squared equals one. This should look very similar to the standard form of a circle. And just like a circle, our center for our lips is the point HK. So if I come back and look at our given equation, what are H and K? Well, I have X plus four That's like X minus negative four. So negative forest is H. And then why minus three XK is three. So that gives me my center. 1234123 The point Negative 43 Now let's come back and look at those denominators. We always use A to denote the biggest denominator So if a is the biggest that is under X, that means that X is my major axis. And I have ah, horizontal um, the lips If they're switched, though, if my biggest denominator is under the why term, Well, that means why is my major axis and I have a vertical ellipse, So knowing where the biggest denominator is indicates the orientation off my ellipse. So let's see what we've been given. My largest denominator is under the X term, so my major access will be parallel to the X axis and A is going to be four. So I go to my center and I'm gonna go along the parallel to the X axis side to side, and I'm going to go four units 1234 on either side of that center. Those are the vergis ease the endpoints of my major axis for my minor axis. That tells me how fat or skinny my ellipses I'm gonna look at the other denominator. And that tells me that B is Chu. So again, starting in my center, I'm going to go up to and down to, and I'm going to connect thes points into an ellipse. So that is the graph off are given equation

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