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