Complex Related Rates: Points A and B move along the x- and y- axes, respectively,...

harveyandstanley

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Points A and B move along the x- and y- axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing and is it increasing or decreasing when OB=2r and B is moving toward o at the rate of 0.3r m/sec?
 
Points A and B move along the x- and y- axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing and is it increasing or decreasing when OB=2r and B is moving toward o at the rate of 0.3r m/sec?

What are your thoughts?

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Points A and B move along the x- and y-axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing...
Which point is "O"? Does this mean "the origin"?

...and is it increasing or decreasing when OB=2r and B is moving toward o...
Does "o" mean "O", or is it a different point?

...at the rate of 0.3r m/sec?
Is the "r" supposed to be in the "rate" expression?

When you reply, please include a clear listing of your thoughts and efforts so far, starting with a scan of (or detailed description of) your initial drawing for this exercise. Thank you! ;)
 
Points A and B move along the x- and y- axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing and is it increasing or decreasing when OB=2r and B is moving toward o at the rate of 0.3r m/sec?

Let the co-ordinate of the point A be[xA,0] and the co-ordinate of the point B be [0,yB].

What is the equation of the line joining A and B?

What is the length of the perpendicular distance of a given point (here (0,0] to a given line (here AB)?
 
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