The y-coordinate of one focus of the ellipse `36x^2+25y^2+144-50y-731=0` is

Options

A. -2
B. 1
C. 3.32
D. 4.32

Answer

D

Explanation

Complete the square and put the equation of the ellipse in standard form:
`36x^2+25y^2+144x-50y-731`
`=36(x+2)^2+25(y-1)^2-900`
`((x+2)^2)/(25)+((y-1)^2)/(36)=1`
The center of the ellipse is at (-2,1), with `a^2=36` and `b^2=25` , and the major axis is parallel to the y-axis. Each focus is `c=sqrt(a^2-B^2)` units above and below the center. Therefore, the y-coordinates of the foci are `1+-sqrt(11)~~4.32`j and -2.32. [13]