Find the equation of tangent and normal to the curve `x^((4)/(3)) + y^((4)/(3))` = 32 at the point (8,8) .

Explanation

Equation of curve
`x^((4)/(3)) + y^((4)/(3)) = 32`
Slope of tangent at P(8,8) = derivate of function at P(8,8) . Differentiating
we get `(4)/(3) x^((1)/(3)) + (4)/(3) y^((1)/(3)) (dy)/(dx) = 0`
`implies (dy)/(dx)|_(8,8) = -((x)/(y))^((1)/(3)) = -1`
Equation of tangent , at P(8,8) is given by
y - 8 = -1(x-8)
`implies x + y = 16`
Equation of normal is given by
`y - y_(0) = -(1)/(((dy)/(dx))_(x_(0), y_(0))) (x-x_(0))`
`implies y - 8 = (-1)/(-1) (x-8)`
`implies y = x`