an engineer designs a satellite dish with a parabolic cross section. The dish is 15 ft wide at the opening and the focus is placed 4 ft from the vertex. find an equation of the parabola.

I know how to work this problem, but how do I know that I use the equation y^2 = 4px instead of x^2 = 4py.

Please help this is so confusing!!!!

Aside from giving a little more info, it doesn't matter which equation you use. That just assigns the variables. Use which feels more comfortable. I'd probably use 4py = x^2.

p is the distance from the vertex to the focus, so

4(4)y = x^2
y = x^2/16

Now for that pesky 15' diameter:
If we want to find how deep the dish is, then y(7.5) = 56.25/16 = 3.5'

Seems the focus is mounted higher than the rim of the dish.

You cannot solve it, without knowing someting more. Is the 15ft width measured in relation to the vertex somehow? There has to be more than the width, it must also containg some measure of depth of the dish.

When dealing with a parabolic dish, it is important to consider the orientation of the parabola. The equation y^2 = 4px is used when the parabola opens horizontally, while x^2 = 4py is used when the parabola opens vertically.

In this case, the dish is designed with a 15 ft width at the opening. Since width refers to the horizontal dimension, we can conclude that the parabola opens horizontally. Therefore, we will use the equation y^2 = 4px.

To find the value of p in the equation, we need to know the distance between the vertex (the lowest point of the dish) and the focus. In this problem, the focus is placed 4 ft from the vertex. Hence, p = 4 in this case.

Plugging in the value of p in the equation y^2 = 4px, we get y^2 = 4(4)x, which simplifies to y^2 = 16x.

Therefore, the equation of the parabola for this satellite dish is y^2 = 16x.

To determine whether to use the equation y^2 = 4px or x^2 = 4py for a parabolic cross section, you need to consider the orientation of the parabola and the direction of its axis.

The equation y^2 = 4px represents a parabola with a vertical axis of symmetry. In this case, the focus (F) is positioned on the positive side of the y-axis, and the vertex (V) is at the origin (0, 0). This equation is typically used when the parabola opens horizontally.

On the other hand, the equation x^2 = 4py represents a parabola with a horizontal axis of symmetry. In this case, the focus (F) is positioned on the positive side of the x-axis, and the vertex (V) is at the origin (0, 0). This equation is used when the parabola opens vertically.

Now, let's apply this knowledge to the problem at hand. The engineer designs a satellite dish with a parabolic cross section that is 15 ft wide at the opening, which is perpendicular to the x-axis. Since the dish has a vertical opening, it means the dish opens horizontally. Therefore, you should use the equation y^2 = 4px.

Given that the dish is 15 ft wide at the opening, we can find the value of p using the coordinates of a point on the parabola. In this case, the focus (F) is placed 4 ft from the vertex, meaning its coordinates are (4, 0). The opening width, which is the distance from the origin (0, 0) to the focus (F), is 4 ft. Therefore, p = opening width / 4 = 4 / 4 = 1.

Now that we have the value of p, we can substitute it into the equation y^2 = 4px to find the final equation:

y^2 = 4(1)(x)
y^2 = 4x

Hence, the equation of the parabola is y^2 = 4x.