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Find the equation of a curve passing th...

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 coordinate of the point is equal to the x coordinate of the point.

Text Solution

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Slopexy=x
`(dy)/(dx)y=x`
ydy=xdx
integrating both side
`y^2/2=x^2/2+c`
`y^2-x^2=C`
P(0,-2)
C=-4
...
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