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The line lx+my+n=0 bisects the angle between a pair of straight lines of which one is px+qy+r=0. Show that the equation to the other line is:- (px+qy+r)(l^2+m^2) -2(lp+mq)(lx+my+n) =0

The line lx+my+n=0 bisects the angle between a pair of straight lines of which one is px+qy+r=0. Show that the equation to the other line is:-
(px+qy+r)(l^2+m^2) -2(lp+mq)(lx+my+n) =0

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
7 years ago
Form a family of straight lines passing through the point of intersection oflx+my+n=0 andpx+qy+r=0.
(px+qy+r)+µ(lx+my+n)=0

Find the angle betweenlx+my+n=0 andpx+qy+r=0 and equate it to the angle between lx+my+n=0 and the family of straight lines[with slope=-(p+µl)/(q+µm)] to get the value ofµ. Put the value ofµ in the eqn of family of straight lines to the get the eqn of the required line.

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