analytic geometry ( hyperbola)

**ampong09** · February 21st 2011, 03:50 AM

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

**tonio** · February 21st 2011, 04:04 AM

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

**ampong09** · February 21st 2011, 04:10 AM

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

**tonio** · February 21st 2011, 04:12 AM

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

**ampong09** · February 21st 2011, 04:21 AM

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

**tonio** · February 21st 2011, 04:26 AM

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

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