A surgical laser is cutting an incision in the eye according to the equation x^2-4y^2=9, y>0.

Question

The incision rates vary to allow for curvature of the eye. When x=5, dx/dt=300 manometers per second. What is dy/dt at that moment?

A. 18.75 manometers per second
B. 93.75 manometers per second
C. 187.5 manometers per second
D. 960 manometers per second

Answer 1

x^2-4y^2=9,
2x dx/dt-8y dy/dt=0
when x=5, solve for y in the original equation, then put y in
2x dx/dt-8y dy/dt=0 and solve for dy/dt