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+ba−b
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B
a−ba+b
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C
a2−b2
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D
a2+b2
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Solution
The correct option is Aa+ba−b Original equation of straight line is : xa+yb=1
Its transformed equation is : xcosα−ysinαa+xsinα+ycosαb=1 ⇒(cosαa+sinαb)x+(cosαb−sinαa)y=1
Given this line has equal intercepts. ∴cosαa+sinαb=cosαb−sinαa ⇒bcosα+asinα=acosα−bsinα ⇒(a−b)cosα=(a+b)sinα ⇒cotα=a+ba−b