Generator point
G = [ 'x' => gmp_init('55066263022277343669578718895168534326250603453777594175500187360389116729240'), 'y' => gmp_init('32670510020758816978083085130507043184471273380659243275938904335757337482424') ];
From my thinking it's location is somewhere like the picture. Am I correct? If not, where is the location of G on curve.
The question's drawing is about the elliptic curve $y^2=x^3+7$ over the (infinite) field of reals $\mathbb R$. In cryptography, we use elliptic curves over a finite field, often a prime field. The equation can be shared, but that does not make the later curve a subset of the former. Thus the drawing is not really for the curve thought in the question. Same for it's would-be generator.
On a (finite) Elliptic Curve as used in cryptography, there is not a single generator; it's conventional.
The question is about secp256k1 which is specified there, including it's conventional generator. For it's special properties, see this question.
