Parallel Planes and Points (3D)

SolfegeDuck
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Homework Statement



Point A (3,2,-1) is equidistant from two planes (parallel), known as P1 and P2. P1 has the equation 2x-y+2z+4 = 0. Find the equation of P2.


Homework Equations



D = abs val(ax_o + by_o + cz_o + d) divided by sqrt (a^2 + b^2 + c^2)

The Attempt at a Solution



I used the distance formula and figured out that the distance between the point and either plane is 2. But what do I do now? I know that the plane I'm looking for, since it's parallel, has a perpendicular vector that is the same as P1, if not a scalar multiple. But what next? Thanks in advance.
 
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Compute a point on the other plane.
 
how do i do that?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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