## Simplifying equation of a parabola

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
maroonblazer
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Joined: Thu Aug 12, 2010 11:16 am
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### Simplifying equation of a parabola

Hi,
The text defines the equation of a parabola as:
$\sqrt{x^2+(y-p)^2} = y+p$

It goes on to say:
By squaring and simplifying we get $x^2 = 4py$.
I'm trying to recreate the steps they took to get from the first form to the second. I start by removing the radical sign by multiplying both sides by $\sqrt{x^2+(y-p)^2}$

but that doesn't seem to lead anywhere useful.

Hints?

Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

### Re: Simplifying equation of a parabola

The text defines the equation of a parabola as:
$\sqrt{x^2+(y-p)^2} = y+p$

It goes on to say:
By squaring and simplifying we get $x^2 = 4py$.
I'm trying to recreate the steps they took to get from the first form to the second. I start by removing the radical sign by multiplying both sides by $\sqrt{x^2+(y-p)^2}$
Try squaring both sides:

$\left(\sqrt{x^2+(y-p)^2\right)^2\, =\, (y+p)^2$
$x^2+(y-p)^2\, =\, y^2+2yp+p^2$

See where that goes.