A point moves so that the angle from the line

namenerk 2021-12-12 Answered
A point moves so that the angle from the line joining it and the origin to the line (3, - 2) and (5, 7) is 45 Find the equation of the locus.
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Expert Answer

Jacob Homer
Answered 2021-12-13 Author has 41 answers

Step 1
Let the coordinate of the moving point be (α, β) and origine (0, 0)
Then slope of the line joining this two point (α, β) (0, 0) is
m1=β0α0=βα
and the slope of the line joining the point (3, -2) and (5, 7) is
m2=7(2)53=92
Now given that the above two lins whose slope are m1, m2 makes an angle 45
Then by angle between two lines formula
tan45=|m1m21+m1m2|
I=|m1m21+m1m2|
When we remove moduls it will give + and -, (Taking + for actuale angle 45)
When + Then 1=m1m21+m1m2
1+m1m2=m1m2
1+βα×92=βα92
2α+9β=2β9α
11α+7β=0
sins (α, β) is arbitry
locus of the point will be
11x+7y=0

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Donald Cheek
Answered 2021-12-14 Author has 41 answers
Step 1
Then, according to the formula for the angle between two lines
tan45=|m1m21+m1m2|
I=|m1m21+m1m2|
If we remove modules, there will be + and -
Then 1=m1m21+m1m2
1+m1m2=m1m2
1+βα×92=βα92
2α+9β2β9α
11α+7β=0
The locus of the point will be
11x+7y=0
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