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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+1b2−1q2equal 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 systems 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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