Given the differential equation of the family of circles with radius of 2 units and whose center's ordinate is always twice the center's abscissa, express the center's abscissa in terms of x, y, and y'.

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Q: Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes…

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Q: Find an equation for the line that is tangent to the curve y=x3 −9x at the point (3,0).

A: Given: The given curve is y=x3-9x and the point 3,0. To find: The main aim is to find the equation…

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Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

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Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

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