Find the standard form of the equation of the ellipse with the given characteristics. vertices: minor axis of length: 6

Question

Find the standard form of the equation of the ellipse with the given characteristics. vertices:  minor axis of length: 6

Quizplus · Accepted Answer

The center of the ellipse is at the midpoint of the line segment joining the vertices, which is (0,0). The length of the minor axis is given as 6, so the half-length of the minor axis is b = 3.

To find the half-length of the major axis, use the formula a^2 - b^2 = c^2, where c is the distance from the center to each vertex. In this case, c = 8 (half the distance between the vertices). So:

a^2 - b^2 = c^2
a^2 - 3^2 = 8^2
a^2 = 73
a ≈ 8.544

Therefore, the standard form of the equation is:

(x^2/a^2) + (y^2/b^2) = 1
(x^2/73) + (y^2/9) = 1

Converting to hexadecimal notation, this becomes:

11eb11e8_19bf_ff34_ad38_b18462a7561b_TB4588_11

Find the Standard Form of the Equation of the Ellipse