JAMB - Mathematics (1999 - No. 23)
Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)
2x + 2y = 9
2x + 3y = 8
2x + y = 9
x + 2y = 8
Explanation
The locus of a point P(x,y) such that PV = PW where V = (1,1) and W = (3,5). This means that the point P moves so that its distance from V and W are equidistance.
PV = PW
\(\sqrt{(x-1)^{2} + (y-1)^{2}} = \sqrt{(x-3)^{2}
+ (y-5)^{2}}\).
Squaring both sides of the equation,
(x-1)2 + (y-1)2 = (x-3)2 + (y-5)2.
x2-2x+1+y2-2y+1 = x2-6x+9+y2-10y+25
Collecting like terms and solving, x + 2y = 8.
PV = PW
\(\sqrt{(x-1)^{2} + (y-1)^{2}} = \sqrt{(x-3)^{2}
+ (y-5)^{2}}\).
Squaring both sides of the equation,
(x-1)2 + (y-1)2 = (x-3)2 + (y-5)2.
x2-2x+1+y2-2y+1 = x2-6x+9+y2-10y+25
Collecting like terms and solving, x + 2y = 8.
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