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Question Number 101777 by 1549442205 last updated on 04/Jul/20

Find a curve passing through pointA(0;1) for which the triangle formed by the axis Oy ,tangent to the curve at its arbitrary point and the radius−vector of the point of contact,issosceles(and base is the segment of the tangent from the point of contact to the axis Oy)

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{pointA}\left(\mathrm{0};\mathrm{1}\right) \\ $$$$\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{formed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{axis}\:\mathrm{Oy} \\ $$$$,\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{at}\:\mathrm{its}\:\mathrm{arbitrary}\:\mathrm{point} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{radius}−\mathrm{vector}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of} \\ $$$$\mathrm{contact},\mathrm{issosceles}\left(\mathrm{and}\:\mathrm{base}\:\mathrm{is}\:\mathrm{the}\:\mathrm{segment}\right. \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{contact} \\ $$$$\left.\mathrm{to}\:\mathrm{the}\:\mathrm{axis}\:\mathrm{Oy}\right) \\ $$

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