Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and whose latus rectum is 10.
Let the equation of the ellipse is
Then the foci are S(ae, 0) and S’(–ae, 0) length of minor axisBB’ = 2b and length of latus rectum
∴ According to the question
BB’ = SS’
also we have
Putting the value of b from equation (i) in equation (ii), we have
From equation (i), we have
From equation (ii),
Putting the values of a and b in , the equation of required ellipse is
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