Answer:
The equation that says P is equidistant from F and the y-axis is
.
(1, 0), (1, 3/2) and (1,6) are three points that are equdistant from F and the y-axis.
Step-by-step explanation:
Let
and
, where
is a point that is equidistant from F and the y-axis. The following vectorial expression must be satisfied to get the location of that point:
![F(x,y)-P(x,y) = P(x,y)-R(x,y)](https://tex.z-dn.net/?f=F%28x%2Cy%29-P%28x%2Cy%29%20%3D%20P%28x%2Cy%29-R%28x%2Cy%29)
![2\cdot P(x,y) = F(x,y)+R(x,y)](https://tex.z-dn.net/?f=2%5Ccdot%20P%28x%2Cy%29%20%3D%20F%28x%2Cy%29%2BR%28x%2Cy%29)
(1)
If we know that
and
, then the resulting vectorial equation is:
![P(x,y) = \left(1,\frac{3}{2} \right)+\left(0, \frac{y'}{2}\right)](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%20%5Cleft%281%2C%5Cfrac%7B3%7D%7B2%7D%20%5Cright%29%2B%5Cleft%280%2C%20%5Cfrac%7By%27%7D%7B2%7D%5Cright%29)
![P(x,y) =\left(1,\frac{3+y'}{2} \right)](https://tex.z-dn.net/?f=P%28x%2Cy%29%20%3D%5Cleft%281%2C%5Cfrac%7B3%2By%27%7D%7B2%7D%20%5Cright%29)
The equation that says P is equidistant from F and the y-axis is
.
If we know that
,
and
, then the coordinates for three points that are equidistant from F and the y-axis:
![P_{1}(x,y) = \left(1,\frac{3+y_{1}'}{2} \right)](https://tex.z-dn.net/?f=P_%7B1%7D%28x%2Cy%29%20%3D%20%5Cleft%281%2C%5Cfrac%7B3%2By_%7B1%7D%27%7D%7B2%7D%20%5Cright%29)
![P_{1}(x,y) = (1,0)](https://tex.z-dn.net/?f=P_%7B1%7D%28x%2Cy%29%20%3D%20%281%2C0%29)
![P_{2}(x,y) = \left(1,\frac{3+y_{2}'}{2} \right)](https://tex.z-dn.net/?f=P_%7B2%7D%28x%2Cy%29%20%3D%20%5Cleft%281%2C%5Cfrac%7B3%2By_%7B2%7D%27%7D%7B2%7D%20%5Cright%29)
![P_{2}(x,y) = \left(1,\frac{3}{2} \right)](https://tex.z-dn.net/?f=P_%7B2%7D%28x%2Cy%29%20%3D%20%5Cleft%281%2C%5Cfrac%7B3%7D%7B2%7D%20%5Cright%29)
![P_{3}(x,y) = \left(1,\frac{3+y_{3}'}{2} \right)](https://tex.z-dn.net/?f=P_%7B3%7D%28x%2Cy%29%20%3D%20%5Cleft%281%2C%5Cfrac%7B3%2By_%7B3%7D%27%7D%7B2%7D%20%5Cright%29)
![P_{3}(x,y) = \left(1,6 \right)](https://tex.z-dn.net/?f=P_%7B3%7D%28x%2Cy%29%20%3D%20%5Cleft%281%2C6%20%5Cright%29)
(1, 0), (1, 3/2) and (1,6) are three points that are equdistant from F and the y-axis.