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S is the point (4,0) and M is the foot of the perpendicular drawn from a point P to the y-axis. If P moves such that the distance PS and PM remain equal, find the locus of P

S is the point (4,0) and M is the foot of the perpendicular drawn from a point P to the y-axis. If P moves such that the distance PS and PM remain equal, find the locus of P

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Nikhil
 
the locus is a parabola, as you can see from the definitions of the parabola. The directrix is the line x=0. 

Use what you know about the equation 

y^2 = 4px 

In this case, the focus is at (4,0), so the vertex has been shifted to (2,0) and the equation is 

y^2 = 4p(x-2) 

Now figure out the value of p and you're done.
 
Regards
Arun (askIITians forum expert)

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