SOLUTION: The Point P(2,y) equidistant from point F(3,0) and the line with equation x=-3/2. What is the value of y of the point P?

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Question 1163107: The Point P(2,y) equidistant from point F(3,0) and the line with equation
x=-3/2. What is the value of y of the point P?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You can first use the distance formula definition of parabola having focus (3,0) and directrix (-3/2,y), here y NOT being the same as in point P. Simplify as you like, and then find the missing coordinate of point P.


FINDING THE EQUATION
%28x-3%29%5E2%2B%28y-0%29%5E2=%28x-%28-3%2F2%29%29%5E2%2B%28y-y%29%5E2
%28x-3%29%5E2%2By%5E2=%28x%2B3%2F2%29%5E2
x%5E2-6x%2B9%2By%5E2=x%5E2%2B%286%2F2%29x%2B9%2F4
-6x%2B9%2By%5E2=3x%2B9%2F4
-9x%2By%5E2%2B9-9%2F4=0
-36x%2B4y%5E2%2B36-9=0
-36x%2B4y%5E2%2B27=0
highlight_green%284y%5E2=36x-27%29

Now, for point P(2,y), what is (or are) the value of y when x is 2 ?

Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.

The distance from the point P(2,y) to the straight line x = -3/2 is equal to 2 - (-3/2) = 3.5.


The distance between the points  P(2,y) and F(3,0)  is  sqrt%28%283-2%29%5E2%2B%280-y%29%5E2%29 = sqrt%281+%2B+y%5E2%29.


Therefore, the equation to find "y" is


    3.5 = sqrt%281%2By%5E2%29,


or, squaring both sides


    3.5^2 = 1 + y^2,


which implies


    y^2 = 3.5^2 - 1,  y = +/- sqrt%283.5%5E2-1%29 = +/- 3.3541 (approximately).     ANSWER

Solved.

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Be aware (!) The "solution" by @josgarithmetic is wrong starting from the first formula / (line).

For your safety, simply ignore it (!)