find the tangent lines of $9x^2 + 16y^2 = 52$ that are parallel to the line $9x-8y = 1$.
I have differentiated the first function to get $-\dfrac{9x}{16y}$ now I'm not sure how to relate this gradient to the second equation to get the tangent lines that are parallel.
Well you said two lines are parallel if they have the same slope... So we know y' represents the slope of the tangent line... So find y' and set equal to the slope of the line given to you.