Given a plane equation (ax+by+cz=d), how does one find a point on the plane (x0, y0,z0)?

Question

Given a plane equation in the form ax+by+cz=d, how can one find the point (x0, y0, z0)?

I already know what the a,b,c,d coeffiecients are. I am not referring to the x,y,z intercepts

ie. d=-ax0-by0-cz0 See the example here on wolfram

http://mathworld.wolfram.com/Plane.html

Answer 1

I would simply replace $(x,y)\,$ by $\,(x_0,y_0),\,$ i.e $\;ax_0 + by_0 + cz + d = 0,\;$ and solve the equation for $z_0.$

Answer 2

I don't think there's such thing as "The point" on a plane. There are many points and not a special one. However, you can preset 2 of the 3 coords of a particular point on the plane, and find the other one by substituting in the equation.

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Any further explanation needs more detailing about what you're trying to accomplish.