Binomial Theorem

Question
CBSEENMA11015177

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

Sponsor Area

Some More Questions From Binomial Theorem Chapter