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July 13th, 2017, 10:17 PM   #1
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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.
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July 14th, 2017, 03:38 AM   #2
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Quote:
Originally Posted by Anvi View Post
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.
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July 14th, 2017, 04:17 AM   #3
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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).
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July 14th, 2017, 04:25 AM   #4
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Quote:
Originally Posted by skipjack View Post
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.
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July 15th, 2017, 04:19 AM   #5
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Quote:
Originally Posted by Anvi View Post
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.
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