Math, asked by pinkkk89, 11 months ago

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

Answers

Answered by QueenOfKnowledge
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}

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