Exactly. Ill do the soln now.You got x^2/25 + y^2/16 =1
Sub in y=mx+b and you get a quadratic in x. Make the discriminant equal to 0. You now have the general tangent. It should be something like y=mx+-sqrt(16m^2 + 25).
Since m=1, y=x+-sqrt(41)
You love it xDand, in the interests of visualisation: