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प्रश्न
Find the equation for the ellipse that satisfies the given conditions:
b = 3, c = 4, centre at the origin; foci on the x axis.
उत्तर
It is given that b = 3, c = 4, centre at the origin; foci on the x axis.
Since the foci are on the x-axis, the major axis is along the x-axis.
Therefore, the equation of the ellipse will be of the form `x^2/a^2 + y^2/b^2 = 1` where a is the semi-major axis.
Accordingly, b = 3, c = 4.
It is known that a2 = b2 + c2
∴ a2 = 32 + 42 = 9 + 16 = 25
= a = 5
Thus, the equation of the ellipse is `x^2/5^2 + y^2/3^2` or `x^2/25 + y^2/9 = 1`.
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