In Exercises 37–50, graph each ellipse and give the location of i...

Question

In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 1)²/2 + (y +3)² /5= 1

Graph of an ellipse with equation (x-2)²/7 + (y+1)²/11 = 1, showing its foci.

Accepted Answer

Graft the given ellipse and indicate its our equation X minus two squared divided by seven plus Y plus one squared divided by 11 as equals to one. Now, I've changed the order of our equation because you notice the number under our Y squared is larger than the number under our X squared. And the general form of ellipse, we have this form here when our A squared is under our Y, this means we have a vertically oriented lips with our longer major axis, our semi major axis rather under the Y so we can find the center or via ellipse. Now, our center is given by H K, we look in our equation, Our H is two AK is -1. You know, the sin A squared Will be equals to 11, which means our a is a square of 11. So the end points of our lips will occur at H comma K plus A N H comma K minus A. We have two, neither one plus squared of 11 and two negative one minus the square of 11, which if we were to estimate we get two -4. and two, 2.317. Now we can find our site on our pro we will take the equation for linear eccentricity, which is given by C as equals to the square root of A squared minus B squared, C equals square root. We know A squared is 11 B squared is seven which is C is equals to the square root of four, which is two. Our P syin are given by H K plus C and H K minus C because we are having a vertically oriented ellipse two n 1 plus two And 2 - -2. A then occur at 2 - into what you look at our possible graphs. We can then tell the only graph that has all of our points is graph D. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 1)²/2 + (y +3)² /5= 1

Key Concepts

Ellipse Equation

Foci of an Ellipse

Graphing an Ellipse

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