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Find an equation of the tangent line to the curve x2a2−y2b2=1 at the point (x0,y0).

User Mabroukb
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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).

User Chris Rasco
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