Final answer:
The question asks for a parametric equation for a line perpendicular to an ellipse at a specific point, which involves calculus to find the gradient at that point and construct the parametric equations.
Step-by-step explanation:
The question involves finding a parametric equation for the line that is perpendicular to the given ellipse at a specific point. The equation of the ellipse provided is 4x² + 3y² + 2x² = 50, which can be simplified to 6x² + 3y² = 50.
First, to find the line perpendicular to the ellipse at point (3, 2.3), we need to calculate the gradient of the ellipse at that point. This involves finding the partial derivatives dx and dy. Since an explicit function y(x) is not provided, we would use the gradient of the normal to the surface of the ellipse (the normal vector) at the given point to establish the direction of our line.
The equation of the best-fit line for another example provided is not necessary to solve the parametric equations for the perpendicular line to the ellipse.
The step-by-step solution would require calculus knowledge, specifically in dealing with gradients of curves, and constructing parametric equations for lines in two-dimensional space.