SOLUTION: Determine the formula of the parabola with vertex F(1,3) and directrix x=3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine the formula of the parabola with vertex F(1,3) and directrix x=3      Log On


   

Question 1199121: Determine the formula of the parabola with vertex F(1,3) and directrix x=3
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Most any intermediate algebra book would show how this derivation works. Few minutes of study and you can do this yourself. DISTANCE FORMULA! Definition of Parabola!

Equation for the set of points equally distant from (1,3) and (3,y)

%28x-1%29%5E2%2B%28y-3%29%5E2=%28x-3%29%5E2%2B%28y-y%29%5E2
.
.
.
.
highlight%28-4%28x-2%29=%28y-3%29%5E2%29


-

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

vertex should be V, not F
the formula of the parabola with vertex V(1,3) and directrix x=3
%28y-k%29%5E2=-4a%28x-h%29+
where a is the distance between directrix and vertex
directrix x=3=>one point on directrix is (3,3)
other point is (1,3)

a=sqrt%28%283-1%29%5E2%2B%283-3%29%5E2%29
a=sqrt%284%29
a=2
%28y-3%29%5E2=-4%282%29%28x-1%29
%28y-3%29%5E2=-8%28x-1%29