The equation for the tangent line

Question

Use implicit differentiation to find an equation of the tangent line to the ellipse defined by 3x^2+5xy+3y^2=53 at the point (-5,1) .

Answer 1

Implicit differentiation with respect to x:

6x + 5y + 5x dy/dx + 6y dy/dx = 0

dy/dx = ( 6x - 5y)/(5x + 6y) put in the values to find the slope, m (= dy/dx) of the line at (x,y) = (-5,1)

You can then write the line in a point slope form:

y -1 = m (x+5)