Question

Find the equation to the locus of point P from which the distance to (2,0) is equal to the distance from P to the y axis

Answer 1

Answer:

Step-by-step explanation:

y2=4(x−1)≡f(x(t),y(t))=(1+t2,2t) .

Knowing that the distance to the point (2,0) is the same as the distance to the y-axis, gives us

(x−2)2+(y−0)2−−−−−−−−−−−−−−−√=x2+02−−−−−−√.

Solving gives us

y2=4(x−1),

which is a parabola with foci (2,0) and directrix x=0.

To more easily graph, we can find a parametric form of the equation by letting y=2t and then solving for x=1+t2.