Question

What is the equation for the ellipse with horizontal minor axis of length 8 and foci located at (0, 5) and (0, −5).

Answer 1

the center is (0,0); along the y axis

the minor spread is 4

x^2 y^2
---- + ---- = 1
16 a^2


a = the hyp of a right triangle with legs b and foci distance from center (5)

a^2 = b^2 + c^2

a^2 = 16 + 25 = 41


x^2 y^2
---- + ---- = 1 ; it shoud be lol
16 41