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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 eqn of 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 eqn of other line is
(px+qy+r)(l2+m2) -2 (lp+mq)(lx+my+n)=0

Grade:11

1 Answers

Arun
25758 Points
3 years ago
Dear student
 
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)=0Find 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. RegardsArun

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