Question 1081143
Set of points  (x,y) equally distant from line y=8/3 as from point  ( -3/2, 4).  


 Distance Formula and definition for parabola:
{{{sqrt((x-x)^2+(y-8/3)^2)=sqrt((x-(-3/2))^2+(y-4)^2)}}}


-

{{{(y-8/3)^2=(x+3/2)^2+(y-4)^2}}}

{{{y^2-16y/3+64/9=(x+3/2)^2+y^2-8y+16}}}

{{{-16y/3+64/9+8y-16=(x+3/2)^2}}}

{{{(8-16/3)y+64/9-16=(x+3/2)^2}}}

{{{(-8/3)y+64/9-144/9=(x+3/2)^2}}}

{{{(-8/3)y=(x+3/2)^2+80/9}}}

{{{y=-(3/8)(x+3/2)^2-(3/8)(80/9)}}}

{{{highlight(y=-(3/8)(x+3/2)^2-10/3)}}}-------Not yet in integer coefficients.  Your parts (a) and (b)  look like a separate question from the description written above them.



(a)
What is the given information?  Same as the description shown before it, or is part of  (b) ?



(b)
Follow the description as written and put the information into the Distance Formula.  Simplify the equation.
{{{sqrt((x-(-4))^2+(y-(-1))^2)=(3/2)sqrt((x-5)^2+(y-y)^2)}}}
Work with it!