Question

A line has intercepts a, b on axes when the axes are rotated through an angle $\alpha$, the line makes equal intercepts on axes then $\tan \alpha =$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Equation of the lime $\frac{x}{a}+\frac{y}{b}=1$
Transformed eqution is $\frac{1}{a}(x\cos \alpha -y\sin \alpha )+\frac{1}{b}(x\sin \alpha +y\cos \alpha )=1$
Intercepts are equal
x - coefficient $\equiv$ y - coefficient
$\therefore \tan \alpha =\frac{a-b}{a+b}$