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

Graph is the answer

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Oregon State University

Baylor 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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graph each ellipse.$$\…

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Graph each ellipse.$$\…

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Graph each ellipse.$$<…

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Graph each ellipse. $1…

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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 four plus y squared over 16 equals one and we want to graph this ellipse. Now, to do that, let's take a step back and look at this standard form for an ellipse. So we understand what all these numbers mean Now we're gonna have to fractions. I'm going to start with the numerator is first all right, the denominators in in a moment. My enumerators are X minus h squared. Plus why minus k squared and this adding them together is going to give me one. Now those numerator should look very familiar. Those are very similar to the standard form of a circle. And just like in a circle, the center of my lips is going to be the point HK. So if I look at my given equation here for look at those numerator both h and K R zero, I'm not subtracting anything from X and y so the center of my lips is going to be at the origin. Okay, now let's look at her denominators. We use a to show the biggest number in the denominator. If the biggest denominator is under X. That means the X is my major axis and I'm going toe have ah, horizontal ellipse. I'm gonna race these denominators. What if they're switched? Let's say my biggest term is under the why term or my biggest denominators under my Y term? That means that why is now my major axis and I'm going to have a vertical ellipse. So those denominators tell me the orientation of my lips. Now let's take a look at the Ellipse we were given. The biggest denominator is under the why term? So my major axis is the Y axis and A is the square root of 16 or four. So I'm going to start at that center 0.0 going to go along my major y axis, four units in either direction. Thes are the vergis Ease off my ellipse. Those of the outermost points on the major axis. Now how fat Or how skinny is this lips to find that out? We look at the minor axis under the smaller of the denominators That tells me that B is too so on my lips. I'm going to go out to units on the minor axis from the center going either direction. And now I'm going to connect thes four points into a sketch of an Ellipse. So that is the sketch of the Ellipse for are given equation.

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