E elainess New Member Joined Apr 29, 2008 Messages 1 Gender Undisclosed HSC 2001 Jul 19, 2008 #1 If 'R' is the fixed point (3,2) and 'P' is the movable point (x,y) Find the equation of the locus of 'P' if distance PR is twice the distance from P to y=-1 thankss!
If 'R' is the fixed point (3,2) and 'P' is the movable point (x,y) Find the equation of the locus of 'P' if distance PR is twice the distance from P to y=-1 thankss!
L lolokay Active Member Joined Mar 21, 2008 Messages 1,013 Gender Undisclosed HSC 2009 Jul 19, 2008 #2 the point on line y=-1 will have coordinates (x, -1) by the distance formula.. 2 sqrt[(y- -1)^2 + (x-x)^2] = sqrt[(y-2)^2 + (x-3)^2] squaring both sides, and expanding gives 4y^2 + 8y + 4 = y^2 - 4y + 4 + x^2 - 6x + 9 3y^2 + 12y - x^2 + 6x - 9 = 0 or 3y(y+4) - (x-3)^2 = 0
the point on line y=-1 will have coordinates (x, -1) by the distance formula.. 2 sqrt[(y- -1)^2 + (x-x)^2] = sqrt[(y-2)^2 + (x-3)^2] squaring both sides, and expanding gives 4y^2 + 8y + 4 = y^2 - 4y + 4 + x^2 - 6x + 9 3y^2 + 12y - x^2 + 6x - 9 = 0 or 3y(y+4) - (x-3)^2 = 0
