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Question

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p and q are the intercepts of the line L on the new axes, then 1a2−1p2+1b2−1q2 is equal to


A

-1

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B

0

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C

1

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D

none of these

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Solution

The correct option is B

0


Equation of the line L in the two coordinate system is xa+yb=1, Xp+Yq=1
where (X, Y) are the new coordinates of a point (x, y) when the axes are rotated through a fixed angle, keeping the origin fixed. As the length of the perpendicular from the origin has not changed.
11a2+1b2=11p2+1q2 1a2+1b2=1p2+1q2
or 1a21p2+1b21q2=0


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