# Analytic Goemetry

posted by .

Find the equation of the parabola whose axis is horizontal, vertex on the y-axis and which passes through (2,4) and (8,-2).

• Analytic Goemetry -

the general formula for a parabola with known vertex and horizontal axis is
x = a(y-k)^2 + h, where (h,k) is the vertex

in your case the vertex , being on the y-axis , can be called (0,k) , and the equation would be
x = a(y - k)^2 + 0
for the point (2,4)
2 = a(4-k)^2 (#1)

for the point (8,-2)
8 = a(-2-k)^2 (#2)

divide #2 by #1
4 = (-2-k)^2 / (4-k)^2
4(4-k)^2 = (-2-k)^2
64 - 32k + 4k^2 = 4 + 4k + k^2
3k^2 -36 + 60 = 0
k^2 - 12 + 20 = 0
(k-10)(k-2) = 0
k = 10 or k = 2

if k=2, x = a(y-2)^2
and using (2,4)
2 = a(4-2)^2
a = 1/2 ---------> x = (1/2)(y-2)^2

if k=10 , x = a(y-10)^2
again using (2,4)
2 = a(4-10)^2
a = 1/18 ----------> x= (1/18)(y-10)^2

Notice that there are two possible equations,
btw, I checked both equations using the point(8,-2), it also satisfies both equations.

## Similar Questions

1. ### math

write an equation for the parabola with focus (1,3) and vetex (0,3) See the paragraph Analytic Geometry Equations. You will have a choice of equations, you did not state whether the axis of symettry was parallel to x or y axis. http://en.wikipedia.org/wiki/Parabola …
2. ### Algebra2/Trig

Find an equation of the parabola with vertex at the origin. Passes through the point (4,6); horizontal axis. I know it has to be y^2=4px. But I don't know what to do with (4,6). Please show step by step. Thanks.
3. ### algebra

I would like to have some help on this problem please. I'm so post to find the vertex and axis of the parabola.Does anyone have an idea?
4. ### Analytic Goemetry

Find the equation of the parabola with axis parallel to the x-axis and passing through (3/2,1),(5,0) and (-1,2).
5. ### 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?
6. ### Analytic Geometry

Find the equation of the parabola through (-15/4 ,2) and (0,-1) whose axis is parallel to the x-axis and the latus rectum equal to 4
7. ### math

1 identify the coordinates of the vertex and the equation of the axis of summetry of the parabola x=2 (y-1)^2+3 A. The vertex of the parabola is (1,3), and the equation of the axis of symmetry B. the vertex of the parabola is (3,1) …
8. ### geometry

a parabola whose axis is parallel to the y axis passess through the points {1,1), (2.2) and (-1,5). Find the equation of the parabola
9. ### Math

Find the equation of the parabola whose axis of symmetry is horizontal and passes through the points (1, 2), (3, -2) and (7, -6).
10. ### Analytic Geometry

Find the standard and general equation of a parabola with a vertex at (0,0) and graph passing through (3,5) Axis of Symmetry at x-axis.

More Similar Questions