Maths
General
Easy
Question
Line makes angle with If these lines and the line are concurrent, then


 2

The correct answer is:
We should find some relation between a and b using given conditions
Lines $xcosα+ysinα=p$ and$xsinα−ycosα=0$ are mutually perpendicular. Thus $ax+by+p=0$will be equally inclined to these lines and would be the angle bisector of these lines. Now equations of angle bisectors is
$xsinα−ycosα=±(xcosα+ysinα−p)$
$x(cosα−sinα)+y(cosα+sinα)=p$
or
$x(sinα+cosα)−y(cosα−sinα)=p$
Comparing these lines with$ax+by+p=0$, we get
$cosα−sinαa =sinα+cosαb =−1$
$2+2=2$
or
$cosα+sinαa =−sinα+cosαb =−1$
$2+2=2$
Hence option 2 is correct
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