# 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?

Mar 11, 2018

${\left(x - 2\right)}^{2} / 4 + {\left(y + 3\right)}^{2} / 25 = 1$

#### Explanation:

Given: vertical ellipse with center:$\left(2 , - 3\right)$, major axis $= 10$, minor axis $= 4$

vertical axis ellipse equation: ${\left(x - h\right)}^{2} / {b}^{2} + {\left(y - k\right)}^{2} / {a}^{2} = 1$

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

a = 10/2 = 5; " "a^2 = 25; $\text{ "b = 4/2 = 2; " } {b}^{2} = 4$

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

vertical axis ellipse equation: ${\left(x - 2\right)}^{2} / 4 + {\left(y + 3\right)}^{2} / 25 = 1$