In Exercises 19–24, find the standard form of the equation of eac...

Question

In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci.

Accepted Answer

The graph of the ellipse is given below bind its standard equation and the coordinate of the pro now, we know the standard equation of an ellipse is given by the formula X minus H squared divided by A squared plus Y minus K squared divided by B squared as equals to one. Now, based on the graph here, we can find our A squared and our B square. Now this is the horizontally oriented E lips, which means our A squared or A will be horizontal. The A is a distance from the center to one of the ends of the ellipse. Same thing with B B, the distance from the center to the other part of our lips in the right direction. We know it here are A will be 13. If we were to take distance from these two points, we get 13 or B, our distance between Y value is three and Y value is eight will be five. We can then set up our equation. We also know H K is our center Which is 2, 3. Our equation then will be X minus two squared Divided by squared plus Y -3 Squared. Divided by five square. We're gonna simplify this. We should get X -2 squared, Followed by 169 Plus Y - Squared divided by 25. That is set equals to one. Also find their focus using the linear Centricity equation C is equals to A squared minus B squared because this is a horizontal ellipse. A squared is first Square root of 169 March 25 gives us a square root 1 44 which is 12. Our focus then our will be given. Bye H plus C K N H minus C K. Now our age is two. They have two plus 12, three, 10 : -12. 3. Our focus then occur at 14, 3 And -10 3. We now have our equation And we have our two. You look at the possible answers to this problem. They correspond with answer C OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci.