A point is moving along the circle x2 + (y − 2)2 = 2 in such a way that its x-coordinate is decreasing at a rate of 6 unit per second. What is happening to the y-coordinate at the instant when the point has reached
(−1, 3)

Question

A point is moving along the circle x2 + (y − 2)2 = 2 in such a way that its x-coordinate is decreasing at a rate of 6 unit per second. What is happening to the y-coordinate at the instant when the point has reached
(−1, 3)

amistre64 · Answer

if we take the derivative implicitly for time, and plug in the values we get the results

amistre64 · Answer

2xx' + 2y'(y-2) = 0

xx' + y'(y-2) = 0

y'(y-2) = -xx'

y' = -xx'/(y-2)

we are told x' = -6, x=-1, y=3