Question
With the given information below, write the standard form equation for the parabola.
1.) Vertex: (-1,2)
Focus(-1,0)
2.) Vertex: (-2,1)
Directrix x=1
1.) Vertex: (-1,2)
Focus(-1,0)
2.) Vertex: (-2,1)
Directrix x=1
Answers
Reiny
the parabola is vertical, and opens downwards
standard form x^2 = 4py
but vertex is (-1,2)
(x+1)^2 = 4p(y-2)
but p = -2
(x+1)^2 = -8(y-2)
(x+1)^2 = -8y + 16
8y = -(x+1)^2 + 16
y = (-1/8)(x+1)^2 - 2
for the 2nd , use y^2 = 4px and follow the above steps
standard form x^2 = 4py
but vertex is (-1,2)
(x+1)^2 = 4p(y-2)
but p = -2
(x+1)^2 = -8(y-2)
(x+1)^2 = -8y + 16
8y = -(x+1)^2 + 16
y = (-1/8)(x+1)^2 - 2
for the 2nd , use y^2 = 4px and follow the above steps