Find the equation of an ellipse for which c = 4, b = 3, centre is at the origin and foci on x-axis. Determine the eccentricity of the ellipse.

Solution

Equation of ellipse in the standard form is $space space straight x squared over straight a squared plus straight y squared over straight b squared equals 1$ [∵ foci lie on x-axis]
Here, c = 4, b = 3
∴ $straight c squared equals straight a squared minus straight b squared space rightwards double arrow space 16 space equals space straight a squared minus 9 space rightwards double arrow space straight a squared equals 25$
Hence, from (i), equation of ellipse is : $straight x squared over 25 plus straight y squared over 9 equals 1$
Let the eccentricity of the ellipse be e.
∴ c = ae $rightwards double arrow$ 4 = 5e $rightwards double arrow$ $straight e equals 4 over 5$

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Binomial Theorem

Find the equation of an ellipse for which c = 4, b = 3, centre is at the origin and foci on x-axis. Determine the eccentricity of the ellipse.

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