Question 1163107
.
<pre>

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((3-2)^2+(0-y)^2)}}} = {{{sqrt(1 + y^2)}}}.


Therefore, the equation to find "y" is


    3.5 = {{{sqrt(1+y^2)}}},


or, squaring both sides


    3.5^2 = 1 + y^2,


which implies


    y^2 = 3.5^2 - 1,  y = +/- {{{sqrt(3.5^2-1)}}} = +/- 3.3541 (approximately).     <U>ANSWER</U>
</pre>

Solved.


------------


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


For your safety, simply ignore it (!)