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प्रश्न
Find the equation for the ellipse that satisfies the given conditions:
Foci (±3, 0), a = 4
उत्तर
Foci (±3, 0), a = 4
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, c = 3 and a = 4
It is known that a2 = b2 + c2
∴ 42 = b2 + 32
= 16 = b2 + 9
= b2 = 16 - 9 = 7
Thus, the equation of the ellipse is `x^2/16 + y^2/7 = 1`.
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