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Question

A line has intercepts a and b on the coordinate axes. When the axes are rotated through an angle α in anticlockwise direction, keeping the origin fixed, the line makes equal intercepts on the coordinate axes. Then the value of cotα is

A
a+bab
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B
aba+b
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C
a2b2
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D
a2+b2
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Solution

The correct option is A a+bab
Original equation of straight line is :
xa+yb=1
Its transformed equation is :
xcosαysinαa+xsinα+ycosαb=1
(cosαa+sinαb)x+(cosαbsinαa)y=1
Given this line has equal intercepts.
cosαa+sinαb=cosαbsinαa
bcosα+asinα=acosαbsinα
(ab)cosα=(a+b)sinα
cotα=a+bab

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