Find the equation for the ellipse that satisfies the given conditi | Filo

Class 11

Math

3D Geometry

Conic Sections

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Find the equation for the ellipse that satisfies the given conditions: Centre at , major axis on the -axis and passes through the points and

Solution: Since the centre is at and the major axis is on the -axi,s the equation of the ellipse will be of the form,

where is the semi-major axis.
The ellipse passes through points and
Hence,

On solving equations (2) and (3), we obtain  and
Thus the equation of the ellipse is  or
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