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

Class 11

Math

3D Geometry

Conic Sections

558
150

Find the equation for the ellipse that satisfies the given conditions: Major axis on the -axis, centre is origin and passes through the points and

Solution: Since the major axis is on the -axis, 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
Thus the equation of the ellipse is  or
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