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# Line L has intercepts a and b on the coordinate axes. when the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q. Then,

A
a2+b2=p2+q2
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B
1a2+1b2=1p2+1q2
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C
a2+p2=b2+q2
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D
1a2+1p2=1b2+1q2
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Solution

## The correct option is B 1a2+1b2=1p2+1q2 As L has intercepts and b on the axes, the equation of L is xa+yb=1 Let the x-axis and the y-axis be rotated through an angle θ in the anticlockwise direction. In the new system, the intercepts are p and q (OP= p,OQ=q). Therefore , the equation of L w.r.t. new coordinate system becomes xp+yq=1 As the origin is fixed in rotation, the distance of line from the origin in both the cases should be same. Hence, we get d=∣∣∣−1√1a2+1b2∣∣∣=∣∣∣1√1p2+1q2∣∣∣ (Using the formula for distance of a point from a line)or 1a2+1b2=1p2+1q2  Suggest Corrections  0      Similar questions  Related Videos   Straight Line
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