Question

Find the equation whose vertices are (+/- 13,0) and foci are (+/-5,0)​

Answer 1

$\mathfrak\purple{SOLUTION}$

Since the vertices are on x-axis, the equation will be of the form

$\frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1$

where 'a' is the semi-major axis.

Given that a = 13, c = +/-5

•°•, from the relation

${c}^{2} = {a}^{2} - {b}^{2} ... \: we \: get$

$25 = 169 - {b}^{2} \: i.e. \: b = 12$

Hence the equation of the ellipse is

$\red{\frac{ {x}^{2} }{169} + \frac{ {y}^{2} }{114} = 1}$