# Help with Parabola Question by Monday

In summary, the conversation is about a person seeking help with a question and struggling with it for almost 2 days. The question involves using the slopes of lines to prove that FN is perpendicular to PA, using a property of a parabola to show that two triangles are equal, and relating this to the path of light bouncing off the parabola. The person eventually understands the concept with the help of another person and realizes that the line FP is always the same length as PN.
Can somebody please help me with this question. I keep thinking I have made some progress on it and it turns out to be totally useless work. Spent almost 2 days struggling over this problem and 2 others and they have to be done for Monday. I have scanned in the question below.

http://img168.imageshack.us/img168/241/prob6ud2.jpg

If anyone can help me with this it will be greatly greatly appreciated.

Last edited by a moderator:
considering the gradients of the lines means their slopes. that is, using the slopes show that FN is at right angles with PA.

then you can use a property of a parobala that will let you conclude that triangle PAF is the same as triangle PAN. and so are the corresponding angles.

then you must relate this conclusion to the actual path the ray of light takes when it bounces off the parabola. that is, consider the law of reflection for the flat mirror AP.

abode_x said:
considering the gradients of the lines means their slopes. that is, using the slopes show that FN is at right angles with PA.

then you can use a property of a parobala that will let you conclude that triangle PAF is the same as triangle PAN. and so are the corresponding angles.

then you must relate this conclusion to the actual path the ray of light takes when it bounces off the parabola. that is, consider the law of reflection for the flat mirror AP.

Ok thanks adobe. I have managed to prove that the line FN and PA are perpendicular.

What is the property of the parabola that you mention in the 2nd paragraph? I have barely done any work on this type of stuff in the past so I am not sure about it. Is it that the line FP is always the same length as PN? Or is that not true?

Thanks again.

"Is it that the line FP is always the same length as PN? Or is that not true?"

i think that's it. (look at definition of a parabola)

Ok I've got it, it just clicked in my brain this morning. Thanks a lot adobe.

## What is a parabola?

A parabola is a type of curve that is shaped like a U. It is a two-dimensional shape that can be described by a quadratic function, which is a polynomial with an x squared term.

## How do I graph a parabola?

To graph a parabola, you will need to plot points on a coordinate plane according to the equation of the parabola. You can also use the vertex form of the equation to find the vertex and use symmetry to plot additional points.

## What is the difference between a horizontal and vertical parabola?

A horizontal parabola has a vertex that is either the maximum or minimum point on the graph, while a vertical parabola has a vertex that is on the left or right side of the graph. In other words, the direction of the curve determines whether the parabola is horizontal or vertical.

## How do I find the equation of a parabola given certain points?

To find the equation of a parabola, you will need to use the standard form or vertex form of a quadratic equation. Plug in the given points and solve for the variables to determine the equation of the parabola.

## What are some real-life applications of parabolas?

Parabolas have many real-life applications, such as in architecture, engineering, and physics. They can be used to design arches, bridges, satellite dishes, and other structures that require a strong and stable shape. They also occur in nature, such as the shape of water shooting out of a fountain or the trajectory of a projectile.

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