# Thread: analytic geometry ( hyperbola)

1. ## analytic geometry ( hyperbola)

find the equation of the path of a point that moves so that its distance from (5,0) is 5/4 of its distance from x=16/5

2. Originally Posted by ampong09
find the equation of the path of a point that moves so that its distance from (5,0) is 5/4 of its distance from x=16/5

A generic point $(x,y)\in\mathbb{R}^2$ fulfils the conditions iff $\displaystyle{(x-5)^2+y^2=\frac{25}{16}\left(x-\frac{16}{5}\right)^2$.

That is a canonical hyperbola with x-axis equal to 4 and y-axis equal to ...

Tonio

3. can i have it in the standard form ? x^2/a^2 - y^2/b^2 = 1 ?

4. Originally Posted by ampong09
can i have it in the standard form ? x^2/a^2 - y^2/b^2 = 1 ?

Of course you can: just re-arrange algebraically the equation I gave you.

Tonio

5. does this mean something ? http://www.mathhelpforum.com/math-he...5a4348339b.png it's my first time to use this in an equation. thanks for the answer

6. Originally Posted by ampong09
does this mean something ? http://www.mathhelpforum.com/math-he...5a4348339b.png it's my first time to use this in an equation. thanks for the answer

That is what we use to symbolize a point in the plane $\mathbb{R}^2$... What is your level of mathematics?

If you're doing analytic geometry you should understand the above, even if the symbology isn't known to you.

Tonio