Posted by Jody on Friday, April 25, 2008 at 5:29pm.
the focus is at y = 0 and the directrix is at y = 2 so the parabola opens down (sheds water.)
The distance from the focus to the vertex is the same as from the directrix to the vertex ( call it a ) so the vertex is at (4,1), halfway between directrix and focus
now so a = 1 but if parabola is upside down, use negative a so a = -1
with vertex at (h,k) which is (4,1)
form is
(x-h)^2 = 4 (a)(y-k)
(x-4)^2 = -4 (y-1)
x^2 - 8x + 16 = -4 y + 4
- 4 y = x^2 - 8 x + 16
y = -(x^2)/4 + 2 x - 4
e1) 16x^2+9y^2=144
this is an ellipse
(16/144)x^2 + (9/144) y^2 = 1
x^2/3^2 + y^2/4^2 = 1
center at (0,0)
x half axis 3
y half axis 4
e2) x^2/3^2 - (y+2)^2/3^2 = 1
hyperbola
center at (0, -2)
slopes of asymptotes = 3/3 = 1 (or -1)
vertex at (3,-2) and at (-3,-2)
Related Questions
algebra - 6. Find the equation of each parabola described below. a) parabola ...
maths - Given that the equation of the parabola is 5y^2 + 24x = 0. Find (1)The ...
algebra 2 - Directions: The focus and directrix of a parabola are given. Write ...
Algebra - Can someone tell me if I am right? I need to find the equation of a ...
algebra problem - I need to find the equation of a parabola. I am not sure if ...
algebra - How would one write the equation of a parabola whose directrix is y=-6...
algebra - A few more question Id like for someone to check please. 1) what are ...
Math - determine vertex, focus and directrix of parabola. then graph the ...
Pre Cal - write the equations of the parabola, the directrix, and the axis of ...
Algebra II - Write an equation for the parabola with focus (1,3) and vertex (0,3...
For Further Reading
