Equation of the ellipse whose foci are `(2, 2) and (4, 2)` and the major axis is of length `10` is

Options

A. `((x+3)^(2))/(24)+((y+2)^(2))/(25)=1`
B. `((x-3)^(2))/(24)+((y-2)^(2))/(25)=1`
C. `((x+3)^(2))/(25)+((y+2)^(2))/(24)=1`
D. `((x-3)^(2))/(25)+((y-2)^(2))/(24)=1`

Answer

D

Explanation

Since, given that foci of an ellipse are (2, 2) and (4, 2) and length of major axis is 10.
`implies" "2ae=2" "...(i)`
and `" "2a=10`
`implies" "a=5" "...(ii)`
From Eqs. (i) and (ii),
`2xx5xxe=2`
`implies" "e=(1)/(5)`
`because" "b^(2)=a^(2)(1-e^(2))`
`because" "b^(2)=25(1-(1)/(25))=24`
and centre of an ellipse = mid-point of foci = (3, 2) Equation of an ellipse is
`((x-3)^(2))/(25)+((y-2)^(2))/(24)=1`