A few days ago
Pre-calc help…?
A curve is traced by a point P(x,y) which moves such that its distance from the point A (-1,1) is three times its distance from the point B (2,-1). Determine the equation of the curve
Top 1 Answers
A few days ago
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Distance from A in the X-direction is [x-(-1)], in the Y: [y-1]
Using Pythagoras, the straight-line distance is sqrt[(x+1)^2+(y-1)^2]
Using the same logic for the distance to B you get:
sqrt[(x-2)^2+(y+1)^2]
Since distance to A is 3 times the distance to B:
sqrt[(x+1)^2+(y-1)^2]=3*sqrt[(x-2)^2+(y+1)^2]
Squaring both sides yields:
(x+1)^2+(y-1)^2 = 9*[(x-2)^2+(y+1)^2]
expanding the squares and distributing the 9:
x^2+2x+1+y^2-2y+1 = 9x^2-36x+36+9y^2+18y+9
simplifying:
8x^2 – 38x + 8y^2 + 16y + 43 = 0
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