Quick question (possible answers provided). Please HELP.?

Question

A point is moving along a branch of the hyperbola defined by 16x^2 – y^2 = -36. What is dy/dt at point 2, -10, and dx/dt = -1

a) 1.6
b) 3.2
c) 0
d) -3.2

Answer 1

Differentiate both sides with respect to t:

32x(dx/dt)-2y(dy/dt)=0

Plug in what you know:

32(2)(-1) - 2(-10)(dy/dt)=0

Solve for dy/dt:

20dy/dt=64

dy/dt=3.2

Answer 2

32xdx/dt-2ydy/dt=0
so dy/dt=16x/y*dx/dt=2/(-10)(-1)*16=
16/5=3.2