# Find the coordinated of a point.

1. Mar 2, 2013

### VertexOperator

1. The problem statement, all variables and given/known data

Find the coordinates of point Q if Q divides the line AP in the ratio a^{2}:b^{2}, b>a.

2. Relevant equations

http://i.imgur.com/g45qxl6.png

3. The attempt at a solution

I found the equation of PA which was y-btanθ=(bsecθ)/(asecθ)(x-asecθ) than I didn't know what to do.
This is supposed to be a very easy question but I'm not good at conics, I'm much better at calculus/analysis :)

2. Mar 2, 2013

### HallsofIvy

Staff Emeritus
To say that Q is such that it divides the interval, AP, in the ratio x:y means that we must have |AQ|/|AP|= x/(x+y) and, as a result, |QP|/|AP|= y/(x+y).

Here, |AB| is the length of the interval so that we must have |AQ|+ |QP|= |AP|.

From your picture, as well as your refernce to "conics", it appears that A and B are the vertices of an hyperbola and P a point on that hyperbola but you don't seem to have used that fact anywhere.

Last edited: Mar 2, 2013