Question

Find the eq of ellipse whose centre focus and vertex is given

Answer 1

Here is your answer..

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where the equation is given.

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Answer 2

Let us assume that foci of the ellipse are given as : (3,0),(−3,0)(3,0),(−3,0)
And the vertex given is : (5,0)(5,0)
(I have assumed these values for the sake of simplicity)
Now we know that the centre of Ellipse is the mid point of the foci.
Hence in this case centre is : (0,0)(0,0)
We also know that the distance between the centre and vertex is the length of semi-major axis.
So the length of semi-major axis is 5 units in this case.
But the distance between centre and the focus is ‘ae’.
(Here ‘a’ is the length of semi-major axis and ‘e’ is eccentricity)
⇒ae=3⇒ae=3
⇒5e=3⇒5e=3
⇒e=35⇒e=35
Now the using the relation between a,e,b
⇒e=1−b2a2−−−−−√⇒e=1−b2a2
⇒35=1−b225−−−−−√⇒35=1−b225
⇒b=4⇒b=4
We have now found the required things for writing the equation of ellipse.
x225+y216=1x225+y216=1is the required equation.
By using the above method you can find equation of ellipse with any given data.

hope it works ☝️

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