Find the equation of the tangent and normal to the curve x²/a² - y²/b² = 1 at point (√2a, b).

The slope of the tangent at (√2a, b) to the curve x²/a² - y²/b² = 1
2x/a² - 2yy'/b² = 0 ⇒ y' = b²/a²(x/y)|√2a,b = b²/√2a*a²/b = b/√2a
The equation of the tangent: y - b = b/√2a(x - √2a) [Using point-slope form: y - y1 = m(x - x1)]
ay - ab = b/√2x - ab or b/√2x - ay - ab = 0
The slope of the normal = -dx/dy = -√2a/b
Equation of normal: y - b = -√2a/b(x - √2a) ⇒ yb√2 - b²√2 = -ax + √2a² or ⇒ ax + b√2y - √2(a² + b²) = 0.