Loci problem!

ms.cupcake

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Joined
Mar 27, 2013
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point D is (0,4) and variable point F is (2t,0). The perpendicular bisector of DF meet DF at M and the y-axis at R. Find the equation of locus of P as t varies,if P is a midpoint of MR.

The answer is y=2-x^2 but how does it work?help!
 
I will outline the steps I used to solve the problem:

1.) Find the slope of the line segment \(\displaystyle \overline{DF}\), then use the negative reciprocal of this as the slope of the perpendicular bisector.

2.) Use the mid-point formula to determine the coordinates of point \(\displaystyle M\).

3.) Use the slope from 1.) and the point from 2.) in the point slope formula to determine the equation describing the perpendicular bisector.

4.) Determine the coordinates of point\(\displaystyle R\) by letting \(\displaystyle x=0\) in the line from 3.)

5.) Use the mid-point formula to determine the coordinates of point \(\displaystyle P\).

6.) Eliminate the parameter \(\displaystyle t\) to determine the Cartesian equation.

Let us know what you find or if you need further assistance! :D
 
i dont get you at step2. did you use that perpendicular bisector line of DF to find coordinate M ?
 
The perpendicular bisector must pass through the midpoint of \(\displaystyle \overline{DF}\).

What is this point?
 
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