Find exact equation of tangent line and normal line

Question

find equation of tangent line and normal line given x²/25 + y²/9 = 1 with coordinates (5sqrt(2)/2, 3sqrt(2)/2)

Answer 1

Use implicit differentiation to find the derivative formula (y' or dy/dx).

Substitute the x & y values of the stated point, to evaluate m = y' at said point.

 

Eq. of Tangent: y - y₁ = m(x - x₁)

 

calculate n = negative reciprocal of the above m;

Eq. of Normal: y - y₁ = n(x - x₁).

 

Can you do the implicit differentiation?