A-3-dimentional-parabola-f-x-y-z-has-a-focus-P-x-y-z-p-q-r-A-rectangular-box-with-side-lengths-a-b-and-c-see-diagram-has-a-point-P-on-the-front-center-point-of-its-face-If-the-origi

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Question Number 11061 by FilupS last updated on 10/Mar/17

$$\mathrm{A}3\mathrm{dimentional}\mathrm{parabola}f(x,y,z)$$$$\mathrm{has}\mathrm{a}\mathrm{focus}P(x,y,z)=(p,q,r).$$$$$$$$\mathrm{A}\mathrm{rectangular}\mathrm{box}\mathrm{with}\mathrm{side}\mathrm{lengths}$$$$a,b,\mathrm{and}c\left(\mathrm{see}\mathrm{diagram}\right),\mathrm{has}\mathrm{a}\mathrm{point}P$$$$\mathrm{on}\mathrm{the}\mathrm{front}\mathrm{center}\mathrm{point}\mathrm{of}\mathrm{its}\mathrm{face}.$$$$\mathrm{If}\mathrm{the}\mathrm{origin}\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{opposite}\mathrm{face},$$$$\mathrm{in}\mathrm{the}\mathrm{middle},\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{function}\mathrm{of}\mathrm{the}$$$$\mathrm{curve}?$$$$$$$$\mathbf{Note}$$$$\mathrm{Origin}O(x,y,z)=(0,0,0)$$$$O(x,y,z)=(p-c,q,r)$$

Commented by FilupS last updated on 10/Mar/17

Commented by FilupS last updated on 10/Mar/17

$$\mathrm{Let}c\mathrm{be}\mathrm{parallel}\mathrm{to}\mathrm{the}x\mathrm{axis}$$$$\mathrm{Let}a\mathrm{be}\mathrm{parallel}\mathrm{to}\mathrm{the}y\mathrm{axis}$$$$\mathrm{Let}b\mathrm{be}\mathrm{parallel}\mathrm{to}\mathrm{the}z\mathrm{axis}$$

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