Asked by Sally
                Use the distance formula to find the equation of a parabola. Focus: (6,0) and directrix X = -3
I know the distance formula is:
√(x-x1)^2+(y-y1)^2 = √(x-x2)^2+(y-y2)^2
I know I need to sub (6,0) for x1,y1 and (-3,y) for x2,y2
√(x-6)^2+(y-0)^2 = √(x-(-3))^2+(y-y)^2
√(x-6)^2+y^2 = √(x+3)^2
Then I get lost. Please help.
            
            
        I know the distance formula is:
√(x-x1)^2+(y-y1)^2 = √(x-x2)^2+(y-y2)^2
I know I need to sub (6,0) for x1,y1 and (-3,y) for x2,y2
√(x-6)^2+(y-0)^2 = √(x-(-3))^2+(y-y)^2
√(x-6)^2+y^2 = √(x+3)^2
Then I get lost. Please help.
Answers
                    Answered by
            MathMate
            
    focus(6,0), directrix x=-3 means 
If the distances are equal, then the squares of the distances from directrix and focus are also equal, so
(x-(-3))²=(x-6)^2+(y-0)^2
(x+3)²-(x-6)²=y²
Factor by difference of two squares
18(x-1.5)=y²
(x-1.5)=y²/(4*4.5)
h=1.5, c=4.5 for (x-h)=y²/4c
meaning the vertex is at (1.5,0) and distance from vertex to directrix is 4.5.
    
If the distances are equal, then the squares of the distances from directrix and focus are also equal, so
(x-(-3))²=(x-6)^2+(y-0)^2
(x+3)²-(x-6)²=y²
Factor by difference of two squares
18(x-1.5)=y²
(x-1.5)=y²/(4*4.5)
h=1.5, c=4.5 for (x-h)=y²/4c
meaning the vertex is at (1.5,0) and distance from vertex to directrix is 4.5.
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