Line 'L' has interceps a and b on the coordinate axis. When the axis are rotated through a given angle, keeping the origin fixed, the same line 'L' has intercepts p and q on the new axis, then

A) a² + b² = p² + q²

B) a² + p² = b² + q²

C) 1/a² + 1/b² = 1/p² + 1/q²

D) 1/a² + 1/p² = 1/b² + 1/q²

hi,

 in the first coordinate sys,

x/a + y/b = 1     ..............................1

in other

x'/ p + y'/q  =1

where

so,  x {  cos θ/p - sinθ /q }   + y { sinθ /p  + cosθ/ q }  =1 

comparing with (1).....

 {  cos θ/p - sinθ /q }/ 1/a   = { sinθ /p  + cosθ/ q }  / 1/b = 1/1

 cos θ/p - sinθ /q   = 1/a  ...............2

sinθ /p  + cosθ/ q  = 1/b ........................3

sq. and adding 2 &3

1/p^2 +  1/q^2  = 1/a^2 + 1/b^2