Consider the ellipse 9 x^2 + 36 y^2 = 64.

Question

the length of its major axe is ?
the length of its minor axe is ?

Answer 1

9x^2 + 36y^2 = 64
When Y = 0,
9x^2 = 64
x^2 = 64/9
X = +- 8/3 = x-intercepts.

When X = 0,
36y^2 = 64
y^2 = 64/36
Y = +- 8/6 = +-4/3 = y-intercepts.

Major Axis = 8/3 - (-8/3)=8/3+8/3= 16/3

Minor Axis = 4/3 - (-4/3) = 8/3.

NOTE: The major axis has the largest
intercept.