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)   (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









Now, for point P(2,y), what is (or are) the value of y when x is 2 ?
Answer by ikleyn(52787)   (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   = .


Therefore, the equation to find "y" is


    3.5 = ,


or, squaring both sides


    3.5^2 = 1 + y^2,


which implies


    y^2 = 3.5^2 - 1,  y = +/-  = +/- 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 (!)



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