Question

Find the standard form of the equation of the ellipse with the following characteristics.

foci: (+/-5, 0) major axis of length: 22

Answer 1

a = 22 / 2 = 11 = radius of major axis.

c^2 = a^2 - b^2.

5^2 = (11)^2 - b^2,
25 = 121 - b^2,
b^2 = 121 - 25,
b^2 = 96,
b = 4*sqrt(6).

STD Form: X^2 / a^2 + Y^2 / b^2 = 1.

X^2 / 121 + Y^2 / 96 = 1.

X^2 / (11)^2 + Y^2 / 4*sqrt(6),