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sketch the graph of the given ellipse, labeling all intercepts.$$\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$$

Graph is the answer

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Missouri State University

McMaster 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).

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sketch the graph of the gi…

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Sketch the graph of each e…

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graph each ellipse.$$\…

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Graph each ellipse.$$\…

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01:17

Graph each ellipse.$$<…

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Sketch a graph of the elli…

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graph each ellipse.$$(…

for this problem, we have been given the equation of an Ellipse X squared over 16 plus y squared over four equals one. And our goal is to sketch this ellipse. Now, in order to do that, let's take a step back and review the standard form for an ellipse so that we understand what all the numbers are in. Our equation on the lips is set up as two fractions. I'm going to write the numerator for the moment. I'm gonna come back to the denominators in a minute. My numerator r x minus h squared Plus why minus k squared. And when we add these fractions, they're going to equal one. So those numerator should look very familiar. It looks very similar to the standard form of a circle. And just like a circle, the center of my lips is going to be the point. H k, Let's take a look at our equation. In this case, H and K are both zero. I'm not subtracting anything from X and y so the center of my lips will be the origin. The 0.0 Now let's go back and look at those denominators. The biggest denominator we did note with a squared. If that biggest number is under my ex term, that means excess my major axis and I have a horizontal ellipse. If I switch these denominators and I put the bigger number under the Y term, that means why is my major axis and I have Ah, horror or I start I have a vertical ellipse. So where the bigger denominator is tells me the orientation of my lips. Well, if I look at what we've been given, the biggest denominator is under the X term. So my major axis is along the X axis and a square to 16, which means a is four. So I'm going to start at the center. On my graph, I'm gonna go along the major axis four units in either direction those air, the vergis ease of my lips. Now how wide or how skinny is my lips will To find that out, we need be, we go to the other denominator, which tells me that B is too. So I'm going to go up two units and down two units on my minor axis and then connect my dots that will give me the sketch of the Ellipse equation that we were given

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