I am studying my for my midterm and have been having troubles with a specific problem. I found the solution for it here, https://socratic.org/questions/the-surface-z-xsqrt-x-y-intersects-the-plane-y-3-along-a-curve-c-how-do-you-find, but I am unsure of how the line is being parameterized. Any help would be appreciated
2026-03-30 05:38:37.1774849117
Parametric equations of the tangent line to a curve
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I am not exactly sure where you are stuck, but usually given a point, let's say $P_o = (x_o, y_o, z_o)$ and vector (aka direction vector) $\vec{v} = (a,b,c)$ then you are interested in all points $P = (x,y,z)$ satisfying $$ P-P_o = t\vec{v} \quad\text{for some}\quad t \in \mathbb R$$ This give us $$ x = x_o + at \\y = y_o + bt \\ z = z_o + ct$$