Find the equation of the ellipse which passes through the point, [4,1] and having its foci at [+-3,0].

Let the equation of the ellipse be 

Let e be the eccentricity.

As the ellipse passes through the point (4, 1), therefore, (4, 1) must satisfy the equation of the ellipse.

 

The foci are given as (±3, 0). 

∴ae = ±3

We know that

Substituting the value of from equation (2) in equation (1), we get

But  can't have the value 8, as then will be negative, therefore, we have

Thus, the equation of the ellipse is given by

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