Question

Write the equation of the ellipse with the endpoints of the major axis (-11, 0) and (11, 0) and minor axis (0, -3) and (0, 3)

Answer 1

Answer:

x/121 + y/9 = 1

Step-by-step explanation:

The major axis is 22 units long, in a horizontal line, and the center is in the middle of the major axis line segment. The center is at the origin. The distance of the whole axis is 22, and its endpoints are 11 units from the center. The axis length is 2a = 22, so a = 11.

Becasue the major axis is horizontal, this ellipse is wider than it is tall.

The minor axis is perpendicular to the major axis and it always shoter (hence the name 'minor'). In this case, it is vertical, is 6 units long, so we say that 6 = 2b, and b = 3.

The ellipse center is (h,k). But in this case, the center is the origin, so h = 0 and k = 0.

The equation for a horizontal ellipse is (x-h)²/a² + (y-k)²/b² = 1, a>b

(x-0)²/11² + (y-0)²/3² = 1

*** x/121 + y/9 = 1

The equation for a vertical ellipse is (x-h)²/b² + (y-k)²/a² = 1, a>b

If the bigger denominator is under 'x' term the ellipse is horizontal, with the longer axis being horizontal.

If the bigger denominator is under the 'y' term, the ellipse is vertical, with the longer axis being vertical.

I'm including 2 files.

The 'brainly ellipse' is form this particular problem.

The 'General Ellipse Info' is a collection of my personal math notes on elleipses.

Hope this helps.

*** Let me try the 2nd attachment again as a PDF. You may not have MS Office 10.