Question

What is the equation of the tangent line to the curve x² y² = 2?

Answer 1

The equation of the tangent line to the curve x²y² = 2 can be found by taking the derivative of the curve equation and evaluating it at a specific point.

Step-by-step explanation:

The equation of the tangent line to the curve x²y² = 2 can be found by taking the derivative of the curve equation and evaluating it at a specific point.

1. Find the derivative of the curve equation using the product rule: 2xy² + 2x²yy' = 0
2. Solve the derivative equation for y' to get y' = -xy/y²
3. Plug in the x-coordinate of the point of tangency into y' to find the slope of the tangent line
4. Use the point-slope form of a line to write the equation of the tangent line: y - y₁ = m(x - x₁)
5. Simplify the equation to obtain the final equation of the tangent line.