Question

How do you write the equation of an ellipse with center at `(2,-3)` the major axis is vertical and is 10 units long, and the minor axis is 4 units?

Answer 1

`(x-2)^2/4 + (y+3)^2/25 = 1`

Explanation:

Given: vertical ellipse with center:`(2, -3)`, major axis `= 10`, minor axis `= 4`

vertical axis ellipse equation: `(x-h)^2/b^2 + (y-k)^2/a^2 = 1`

`" where center"= (h, k); a = ("major axis")/2; b = ("minor axis")/2`

`a = 10/2 = 5; " "a^2 = 25`; `" "b = 4/2 = 2; " "b^2 = 4`

`h = 2; " " k = - -3 = +3`

vertical axis ellipse equation: `(x-2)^2/4 + (y+3)^2/25 = 1`