A line makes intercepts ` a ` and `b` with the coordinate axes. If the coordinate system is rotatedthrough ` 45^@ ` clockwise and the intercepts on the new system become `A ` and ` B,` then which one is true: (i) `1/a^2+1/b^2=1/A^2+1/B^2` (ii) `a^2+b^2=A^2+B^2` (iii) `aA=bB` (iv) none of these

Options

A. `(1)/(a ^(2)) + (1)/(b^(2)) = (1)/(A ^(2)) + (1)/(B ^(2))`
B. `a ^(2) + b ^(2) = A^(2) + B ^(2)`
C. `aA =bB`
D. none of these

Answer

A