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JAMB 2003 · UME · Q31

Find the equation of the locus of a point P(x,y)P(x, y) which is equidistant from Q(0,0)Q(0, 0) and R(2,1)R(2, 1).

Worked solution (try it first)
  1. PQ=PRPQ = PR, so square both distances: x2+y2=(x−2)2+(y−1)2x^2 + y^2 = (x - 2)^2 + (y - 1)^2.
  2. Expand the right side: x2−4x+4+y2−2y+1x^2 - 4x + 4 + y^2 - 2y + 1.
  3. Cancel x2x^2 and y2y^2: 0=−4x−2y+50 = -4x - 2y + 5.
  4. So 4x+2y=54x + 2y = 5, option C.

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