Let `C` be a curve which is the locus of the point of intersection of lines `x=2+m` and `m y=4-mdot` A circle `s: (x-2)^2+(y+1)^2=25` intersects the curve `C` at four points: `P ,Q ,R ,a n dS` . If `O` is center of the curve `C ,` then `O P^2+O Q^2+O R^2+O S^2` is (a) `50` (b) `100` (c) `25` (d) `(25)/2`

Options

A. 50
B. 100
C. 25
D. 25/5

Answer

B

Explanation

`x-2=m`
`y+1=(4)/(m)`
`therefore" "(x-2)(y+1)=4`
`"or "XY=4`
where `X=x-2,Y=y+1`
`S-=(x-2)^(2)+(y+1)^(2)`
= 25 ltBrgt `"or X^(2)+Y^(2)=25`

Curve C and circle S both are concentric. Therefore,
`OP^(2)+OQ^(2)+OR^(2)+OS^(2)=4r^(2)` ltBrgt `=4xx25=100`