Understanding The Parabola $x^2 + 2y = 8x –7$

Question

Now, I am reading S.L. Loney's book on coordinate geometry, and am having a hard time figuring the way he examines parabolas. The standard equation to the parabola is introduced to be $y^2 = 4ax$ where the vertex is the point $(0,0)$, the axis is $y = 0$, and the focus is $(a,0)$. The way Loney solves parabolas is by simplifying them to the standard equation by transforming the origin of coordinates. For example: the parabola $y^2 = 4x + 4y \implies (y – 2)^2 = 4(x + 1)$ is simplified when the origin is shifted to the point $(–1, 2)$. It becomes $y^2 = 4x$ Hence the vertex is $(–1, 2)$, the axis is $y = 2$, and the focus is $(0, 2)$. However, Loney has only given a limited set of examples, and in one of the questions he asks to examine in the same way and find all properties of the parabola $x^2 + 2y = 8x – 7$, I've tried conjuring an idea of my own involving rotating the axes of coordinates, but the process I follow seems to be too lengthy for Loney to intend it, moreover, it doesn't produce any result. Could someone please assist me? Thank you in advance.