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Question

Find the equation of a curve passing through the point (0,-2) given that at any point (x, y)on the curve the product of the slope of its tangent and y co-ordinate of the point is equal to the x co-ordinate of the point.

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Solution

dydxy=x

y dy=x dxy2=x2+c(1)(0,2)lies on (1)4=cy2=x2+4


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