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, thenA) a2 + b2 = p2 + q2B) a2 + p2 = b2 + q2C) 1/a2 + 1/b2 = 1/p2 + 1/q2D) 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

H