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.

Question

Jacob Homer · Accepted Answer

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=β−0α−0=βα and the slope of the line joining the point (3, -2) and (5, 7) is m2=7−(−2)5−3=92 Now given that the above two lins whose slope are m1, m2 makes an angle 45∘ Then by angle between two lines formula tan⁡45∘=|m1−m21+m1m2| ⇒I=|m1−m21+m1m2| When we remove moduls it will give + and -, (Taking + for actuale angle 45∘) When + Then 1=m1−m21+m1m2 ⇒1+m1m2=m1−m2 ⇒1+βα×92=βα−92 ⇒2α+9β=2β−9α ⇒11α+7β=0 ∴ sins (α, β) is arbitry ∴ locus of the point will be 11x+7y=0

Donald Cheek · Accepted Answer

Step 1  Then, according to the formula for the angle between two lines  tan⁡45∘=|m1−m21+m1m2|  I=|m1−m21+m1m2|  If we remove modules, there will be + and -  Then 1=m1−m21+m1m2  1+m1m2=m1−m2  1+βα×92=βα−92  2α+9β−2β−9α  11α+7β=0  The locus of the point will be  11x+7y=0

A point moves so that the angle from the line

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