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 July 13th, 2017, 10:17 PM #1 Newbie   Joined: Jul 2017 From: India Posts: 2 Thanks: 0 Straight lines Hello, I am stuck at these two questions of locus from the topic of straight lines. Q1)A right angled triangle ABC having a right angle at C, CA = b and CB = a, move such that the angular points A and B slide along x- axis and y- axis respectively. Find locus of C. Q2)A variable line L passing through the point B(2,5) intersects the lines 2x² -5xy + 2y² = 0 at P and Q. Find the locus of the point R on L such that distances BP, BR and BQ are in harmonic progression. July 14th, 2017, 03:38 AM   #2
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 Originally Posted by Anvi Hello, I am stuck at these two questions of locus from the topic of straight lines. Q1)A right angled triangle ABC having a right angle at C, CA = b and CB = a, move such that the angular points A and B slide along x- axis and y- axis respectively. Find locus of C. Q2)A variable line L passing through the point B(2,5) intersects the lines 2x² -5xy + 2y² = 0 at P and Q. Find the locus of the point R on L such that distances BP, BR and BQ are in harmonic progression.
Please tell the answer if you know. July 14th, 2017, 04:17 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2216 Q1) I don't understand the description. If A and B move as described arbitrarily, C can be anywhere not on the axes (or C can be where the axes intersect). July 14th, 2017, 04:25 AM   #4
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 Originally Posted by skipjack Q1) I don't understand the description. If A and B move as described arbitrarily, C can be anywhere not on the axes (or C can be where the axes intersect).
Yes I agree Q1) is poorly worded so that the only rational answer is the locus is the entire plane. July 15th, 2017, 04:19 AM   #5
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 Originally Posted by Anvi Hello, I am stuck at these two questions of locus from the topic of straight lines. Q1)A right angled triangle ABC having a right angle at C, CA = b and CB = a, move such that the angular points A and B slide along x- axis and y- axis respectively. Find locus of C.
Since the x and y axes are at right angles, one obvious possibility is that C is the single point (0, 0)! But there are infinitely many other possibilities depending on the rates of motion of A and B and on which side of AB C is.

Quote:
 Q2)A variable line L passing through the point B(2,5) intersects the lines 2x² -5xy + 2y² = 0 at P and Q. Find the locus of the point R on L such that distances BP, BR and BQ are in harmonic progression. Tags lines, straight ,

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### a variable line l passing through the point b (2 5)

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