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Question

Line Lhas intercepts a&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&q, then


A

a2+b2=p2+q2

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B

a2+p2=b2+q2

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C

1a2+1b2=1p2+1q2

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D

none of these

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Solution

The correct option is C

1a2+1b2=1p2+1q2


Explanation for the correct option:

Given that the line L has intercepts a&b.

xa+yb=1...(i)

The axes are rotated through angle α at the origin then the same line L has intercepts p&q

xp+yq=1...(ii)

We Know that line equation is ax+by+c=0and the point having the coordinate x1,y1 then the distance is

d=ax1+by1+ca2+b2

Now consider the equation (i) and find the value of d1

d1=0+0-11a2+1b2d1=-11a2+1b2

Also, consider the equation (ii)and find the value of d2

d2=0+0-11p2+1q2d2=-11p2+1q2

Equating d1&d2

-11a2+1b2=-11p2+1q211a2+1b2=11p2+1q21a2+1b2=1p2+1q2

Hence, option (C) is the correct answer.


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