if `r_(1)` and `r_(2)` are distances of points on the ellipse `5x^(2)+5y^(2)+6xy-8=0` which are at maximum and minimum distance from the origin then

Options

A. `r_(1)+r_(2)=3`
B. `|r_(1)-r_(2)|=1`
C. `|r_(1)-2r_(2)|=0`
D. `r_(1)+2r_(2)=4`

Answer

A, B, C, D

Explanation

Let any point `(rcostheta,rsintheta)` in xy plane
We have to maximize & minimize r
`5r^(2)cos^(2)theta+5r^(2)sin^(2)theta+6r^(2)sinthetacostheta-8=0`
`5r^(2)+3r^(2)sin2theta-8=0`
`r^(2)=(8)/(5+3sin2theta)`
`r_(max)=2`
`r_(min)=1`
`r_(1)+r_(2)=3`