Question

Find the equation of an ellipse, the lengths of whose major and mirror axes are 10 and 8 units respectively.
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Answer 1

AnswEr-

Let the equation of required ellipse is

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

Given:

Length of major axis =10 units....(i)

We know that,

Length of major axis= 2a..(ii)

From eq. (i) and (ii) we get ,

2a=10

⇒a=5

It is also given that ,

Length of minor axis= 8 axis (iii)

We know that,

Length of minor axis = 2b...(iv)

From eq. (iii) and (iv) we get,

2b=8

⇒b=4

Substituting the value of a and b in eq. (a) we get,

$\frac{ {x}^{2} }{ {5}^{2} } + \frac{ {y}^{2} }{ {4}^{2} } = 1$

$\frac{ {x}^{2} }{25} + \frac{ {y}^{2} }{16} = 1$