A particle moves in a circular orbit described by the equation x^2 +y^2=25. As it passes through (4.3), its y coordinate is decreasing at a rate of 3 units/sec. What is the rate of change of the x coordinate the instant the particle is passing through the point (4,3)?
I figured I would dreivate the position equation, x^2 + y^2=25, to arrive at the velocity equation, 2x dx +2y dy, and set that equal to -3, the velocity in the y direction at that point. Of course it doesn't come out right, though, as I am not sure how to account for the velocity in the x direction at that point. How do you separate velocity into x and y components?
Thank you for your help!