Algebra
posted by Jody .
I'm sure how to work the following problems cant anyone help?
1) Write an equation for the parabola with focus (4,0) and directrix y=2.
What do I need to do before I graph the following equations?
e1) 16x^2+9y^2=144
e2) x^2/9  (y+2)^2/9 = 1

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
(xh)^2 = 4 (a)(yk)
(x4)^2 = 4 (y1)
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)
Respond to this Question
Similar Questions

Pre Cal
write the equations of the parabola, the directrix, and the axis of symmetry. vertex: (4,2) focus: (4,6) if someone could explain how to do this problem then that would be great! thanks in advance! Formats to help you find the equation … 
algebra problem
I need to find the equation of a parabola. I am not sure if this is the correct way or if I have the correct answer. Vertex at origin, focus is at (0,3) Equation of parabola vertex (0,0) focus (0,3) focus (h,k+p) (0,0+3) y=03 directrix … 
Algebra
Can someone tell me if I am right? I need to find the equation of a parabola. I am not sure if this is the correct way or if I have the correct answer. Vertex at origin, focus is at (0,3) Equation of parabola vertex (0,0) focus (0,3) 
Math
determine vertex, focus and directrix of parabola. then graph the parabola. first equation: y^2 2x8=0 second equation: y^2 4y 12x= 8 please show your work! 
algebra
6. Find the equation of each parabola described below. a) parabola with vertex (0,0) and the focus (0,7) b) parabola with focus (3,0) and directrix x=3 c) parabola with vertex (3,3) and directrix x=1 d) parabola with focus (2,1) … 
pre cal
What is the center of the conic whose equation is x^2 + 2y^2  6x + 8y = 0 2.Which one of the following equations represents a hyperbola? 
algebra
A few more question Id like for someone to check please. 1) what are the vertex, focus, and directrix of the parabola with the given equation? 
PreCalculus
How do I solve these equations? I need to create an equation given the characteristics? 
precallcuslus
can you check my work and explain the last question because I do not uderstand. Explain what each of the following represents, and how y = a(x  h)2 + k, a ≠ 0 and (x  h)2 = 4p(y  k), p ≠ 0 are equivalent. The equation (x  h)2 … 
precalculs
Explain what each of the following represents, and how equations (a) and (b) are equivalent. (a) y = a(x  h)2 + k, a ≠ 0 (b) (x  h)2 = 4p(y  k), p ≠ 0 (c) (y  k)2 = 4p(x  h), p ≠ 0 can you check my work and explain how equations …