Find the standard form of equation of the ellipse centered at the origin with a vertex located at (17,0) and a focus at (8,0).

Question

Find the standard form of equation of the ellipse centered at the origin with a vertex located at (17,0) and a focus at (8,0).

Answer 1

Hi, there! Ellipse can be a tricky beast to master....

Since your vertex and focus have y-values of 0, that tells us that the ellipse's major axis runs parallel to the x-axis. The standard form equation of an ellipse that follows this is as follows:

x² + y² = 1

a² b²

In this equation, a is the value of the vertices (which we know is 17 because it was given to us in the problem) and b is the value of the co-vertices (which we don't know). To find the value of b we use the following equation:

c²= a² - b²

Again, a is the value of our vertex (17) and c is the value of our focus (8):

(8)² = (17)² - b²

64 = 289 - b²

-225 = - b²

√225 = √b²

15 = b

Now that we've found b, we can plug everything into the standard equation:

x² + y² = 1

(17)² (15)²

x² + y² = 1

289 225

There you have it! I hope this explanation was thorough and answered all of your questions. If you have additional questions please don't hesitate to reach out! Learn on! :)