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Question 71320: For each point in a set of points, its distance from (3,4) is four times its distance from (-5,2). Find the equation and determine what conic section the graph will be.
Answer by sudhir(14)   (Show Source):
You can put this solution on YOUR website! Here two things are at work :-
1) Distance between two points (a,b) & (x,y) = ((x-a)^2 + (y-b)^2)^0.5
2) To get the locus we convert the wordings given in the problem in the form
of an equation.
Now, to solve the problem let's denote a general point by (x,y) so from given condition:-
((x-3)^2 + (y-4)^2)^0.5 = 4((x+5)^2 + (y-2)^2)^0.5
((x-3)^2 + (y-4)^2) = 16((x+5)^2 + (y-2)^2)
x^2+9-6x+y^2+16-8y = 16x^2+16*25+2*16*5x+y^2+4-4y
15x^2 + 166x + 4y + 379 = 0 This is the required equation of locus.
This graph is a parabola
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