79–82. {Use of Tech} Visualizing tangent and normal lines <IMAGE>
a. Determine an equation of the tangent line and the normal line at the given point (x0, y0) on the following curves. (See instructions for Exercises 73–78.)
(x²+y²)² = 25/3 (x²-y²); (x0,y0) = (2,-1) (lemniscate of Bernoulli)

Verified step by step guidance

1. First, differentiate the given implicit equation (x² + y²)² = (25/3)(x² - y²) with respect to x using implicit differentiation to find dy/dx.
2. Evaluate dy/dx at the point (2, -1) to find the slope of the tangent line at that point.
3. Use the point-slope form of the equation of a line, y - y0 = m(x - x0), where m is the slope found in the previous step and (x0, y0) = (2, -1) to write the equation of the tangent line.
4. To find the normal line, remember that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Calculate this slope.
5. Finally, use the point-slope form again with the normal line's slope and the point (2, -1) to write the equation of the normal line.