Question

find the equation of the line tangent to 9x^2+16y^2=52 through (2,-1)

Answer 1

take the derivative wrt x and get
\[18x+32yy'=0\] solve for \(y'\) and get
\[y'=-\frac{18x}{32y}=-\frac{9x}{16y}\]
replace x by 2 and y by -1 to get the slope, then use the point - slope formula

Answer 2

ohhh gotcha. thanks

Answer 3

yw