# How do you write an equation of an ellipse in standard form given vertices are (plus or minus 15,0) and the foci are (plus or minus 9,0)?

Nov 17, 2015

${x}^{2} / 225 + {y}^{2} / 144 = 1$

#### Explanation:

$V : \left(\pm 15 , 0\right)$

$V : \left(h \pm a , k\right)$

$\implies V : \left(0 \pm 15 , 0\right)$

$\implies C : \left(h , k\right) \implies \left(0 , 0\right)$

$a = 15$

$f : \left(h \pm c , k\right)$

$f : \left(\pm 9 , 0\right)$

$\implies c = 9$

${c}^{2} = {a}^{2} - {b}^{2}$

$\implies {b}^{2} = {a}^{2} - {c}^{2}$

$\implies {b}^{2} = {15}^{2} - {9}^{2}$

$\implies {b}^{2} = 225 - 81 = 144$

$\implies b = 12$

Standard equation of a horizontal ellipse is

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

$\implies {\left(x - 0\right)}^{2} / {15}^{2} + {\left(y - 0\right)}^{2} / {9}^{2} = 1$

$\implies {x}^{2} / 225 + {y}^{2} / 144 = 1$