Answer:
To find an equation of the tangent line to the curve x²/a² - y²/b² = 1 at the point (x₀, y₀), we need to use the following steps:
1. Take the derivative of both sides of the equation using implicit differentiation:
d/dx (x²/a² - y²/b²) = d/dx (1)
2x/a² - 2y/b² (dy/dx) = 0
2. Solve for dy/dx to find the slope of the tangent line at the point (x₀, y₀):
(dy/dx) = (x₀/b²)/(y₀/a²) = (x₀a²)/(y₀b²)
3. Use the point-slope form of a line to write an equation for the tangent line:
y - y₀ = (x₀a²)/(y₀b²) (x - x₀)
This is the equation of the tangent line to the curve x²/a² - y²/b² = 1 at the point (x₀, y₀).