Question

Find the lengths of the major and minor axes and the eccentricity of the ellipse `((3x-4y+2)^2)/(16)+((4x+3y-5)^2)/9=1`

Answer 1

Correct Answer - Major axis =8/5, Minor axis `=6//5,e=(sqrt7)/(4)`
the given equation is
`({(3x-4y+2)//5}^(2))/(16//25)+({(4x-3y-5)//5^(2)})/(9//25)=1`
Hence `a^(2)=16//25 and b^(2)=9//25`. Therefore,
Lengths of major aixs `=2a=(8)/(5)`
and length of minor axis `=2b=(6)/(5)`
`e^(2)=1-(9)/(16) or e=(sqrt(7))/(4)`