Question
Download Solution PDFThe foci of an ellipse are (±3, 0) and its eccentricity is 1/3, find its equation.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The general equation of the ellipse is:
Here, coordinates of foci are (±ae, 0).
Also, we have b2 = a2(1 - e2), where e is the eccentricity.
Calculation:
Since the coordinates of the foci are (±3, 0).
⇒ ae = 3
⇒ a × (1/3) = 3 (∵ e = 1/3)
⇒ a = 9
Now, b2 = a2(1 - e2)
⇒ b2 = 72
On putting the value of a2 and b2 in the general equation of an ellipse, we get
Hence, the equation of the ellipse is
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