the geometry of the parabola (1 Viewer)

jnney · Aug 19, 2011

a point P (x,y) moves so that its distance from the point K(2,5) is twice its distance from the line x=-1.

x^2-4x+y^2-10y+29= 4|x^2+1|^2

D:

ohexploitable · Aug 19, 2011

$\sqrt{(x-2)^2+(y-5)^2}=2\times|x-(-1)|$

Expand and simplify lol.

jnney · Aug 19, 2011

ohexploitable said:
$\sqrt{(x-2)^2+(y-5)^2}=2\times|x-(-1)|$

Expand and simplify lol.

Don't you have to sub in P(x,y) on the right hand side?

ohexploitable · Aug 19, 2011

jnney said:
Don't you have to sub in P(x,y) on the right hand side?

I did.

The distance of P(x,y) from the line x=-1 is |x-(-1)|.

ohexploitable · Aug 19, 2011

The distance is independent of the y-value. For example, (2,-5) and (2,449257493879238984) are both 3 units from the line x=-1.

funnytomato · Aug 19, 2011

ohexploitable said:
The distance is independent of the y-value. For example, (2,-5) and (2,449257493879238984) are both 3 units from the line x=-1.

exaxtly, it'd be much easier with a diagram

jnney · Aug 19, 2011

ohexploitable said:
I did.

The distance of P(x,y) from the line x=-1 is |x-(-1)|.

OH i get it, thanks.