Equation of a line through an ellipse's center

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This might be a stupid question but, When trying to find the equation/slope of a line through the middle of an ellipse and any point on the ellipse you have to use two points, (h,k), which stands for the center, and some arbitrary point on the ellipse. Would the point simply be (x,y), (x,f(x)), where f(x) is a placeholder for the standard ellipse equation, or (x,g(x)), where g(x) is a placeholder for the standard ellipse equation solved for y. Thanks