Answer:
1/4.
Step-by-step explanation:
Using implicit differentiation:
2x^2 - xy - y^2 = 15
4x - (x.dy/dx +1.y) - 2y.dy/dx = 0
4x - x.dy/dx - y - 2y.dy/dx =0
-2y.dy/dx - x. dy/dx = y - 4x
dy/dx = (y - 4x)/(-2y - x).
So at the point (2, 5):
dy/dx = (5 - 4(2)) / (-2(5) - 2)
= -3/-12
= 1/4.
