A few days ago
redsox_04_champs

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
crhannem

Favorite Answer

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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