Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. Horizontal major axis of length 8, minor axis of length 3

Question

Find an equation for the ellipse that has its center at the origin and satisfies the given conditions.

Horizontal major axis of length 8, minor axis of length 3

Answer 1

√((x+√55)² + y²) + √((x-√55)² + y²) = 16 or

(8 cos t, 3 sin t) , 0 <= t < 2 π or

x²/64 + y²/9 = 1

Pick the one you prefer.

The first is from the definition of an ellipse as having the sum of the distance from the two foci equal to the distance between the major vertices.

The second is the parametric formula.

The third is the standard form.

Answer 2

[(x - h)² / a²]+ [(y - k)² / b²] = 1, where (h, k) is the center, a is half the major axis, and b is half the minor axis.

(x² / 16) + (y² / 2.25) = 1