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Xy = c² xdy/dx + y = 0 dy/dx = -y/x dy/dx = -b/a {slope at point (a,b)} equation of tangent ; (y-b) = (-b/a)(x-a) ay - ab = -bx + ab bx + ay = 2ab or x/a + y/b = 2

Xy = c² differentiating the above curve at (a,b) we get slope of that tangent at that point x*dy/dx + y = 0 x*dy/dx = -y dy/dx= -y/x slope at the point (a,b) dy/dx = -b/a the equation of the tangent at (a,b) (y-b) = -b/a (x-a) a(y-b)= -b(x-a) ay-ab = -bx +ab bx+ay -2ab = 0 This is equation of tangent at the point (a,b)