Help Analytical Geometry

if the distance from the focus to a point P on the parabola y^2 = 4px is 10, find the coordinate of p.

how to get the coordinates of P? tnx

Find the Equation of the parabola

See if this helps you.

MrYu said:

if the distance from the focus to a point on the parabola y^2 = 4px is 10, find the coordinate of p.

how to get the coordinates of P? tnx

Click to expand...

This question is either poorly phrased or it is a trick question.

1) Is the particular point (that with distance 10 from the focus) on the parabola labeled as P (capital P) and the focus labeled as p (length small p)?

2) Or, are you looking for the coordinates of the focus, which is labeled as p?

Case 1 is solvable, but the question is phased poorly and confusing since P and p are easy to misinterpret. Please specify more clearly. Mike-ML's link will help you solve this.

Case 2 is a trick question because the distance from the focus to a point on the parabola varies and does not give any information about the location of the focus. Here, the coordinates of the focus are very obvious and easily solved.

However, either way, you should make some attempt at the problem, and then we can guide you further. So, clarify the question and make an attempt at the solution is my recommendation.

up.....

Hi,

Let me rephrase the question for you:

"If the distance from the focus to a point P on the parabola y^2 = 4*p*x is 10, find the coordinates of P. How to get the coordinates of P?"

In other words, we are given a parabola that is open to the right, the focus is at the point (p,0), and a point on the parabola is P=(Px,Py)
and we are also given that the distance from the focus at (p,0) to the point on the parabola (Px,Py) is equal to 10. We then have to
find the coordinates of P, so we have to find Px and Py.
One small note here is that because the parabola is open to the right there will be two solutions for Py and one for Px.

In geometry the parabola is often represented as having a focus where p is along one axis and P is the point somewhere on the parabola itself.

i edit the question above, there is missing in the question typo error of my instructor.

Hi,

The equation is given, y^2=4*p*x

That is the equation and it is a parabola open to the right when p>0 and to the left when p<0.
p is the focus along the x axis, so the focal point is at (p,0).