Answer:
Step-by-step explanation:
Let P(x,y) be any point on the parabola.
focus S (0,5)
Directrix y=-5
or y+5=0
let M be foot of perpendicular from P(x,y) on directrix.
SP=[tex]SP=\sqrt{(x-0)^2+(y-5)^2}\\ PM=\frac{y+5}{\sqrt{1} } =y+5[/tex]
SP=PM
SP²=PM²
(x-0)²+(y-5)²=(y+5)²
x²=(y+5)²-(y-5)²
or x²=y²+10y+25-(y²-10y+25)
x²=y²+10y+25-y²+10y-25
x²=20y
Answer:
Parabolic Equation: 20*y = [tex]x^{2}[/tex]
or y = (1/20)*[tex]x^{2}[/tex]
Step-by-step explanation:
general formula for parabolic conic section:
4c *(y - k) = (x - h)^2
y = (1/4c)*(x - h)^2 + k ; a = 1 / 4c
with focus at (h, k + c)
directrix: y = k - c
focus: (0, 5) = (h, k + c)
directrix y = -5 = k - c
so h = 0, 5 = k + c
-5 = k - c
solve the equation 5 = k + c and -5 = k - c
We get: 0 = 2k , k = 0
so c = 5
4*c (y - k) = (x - h)^2
4*5*(y - 0) = (x - 0)^2
20*y = [tex]x^{2}[/tex]
or y = (1/20)*[tex]x^{2}[/tex]
