## Equation of a curve with given equation of slope and passing through a point

Problem
What is the equation of the curve passing through the point (3, -2) and having a slope at any point (x, y) equal to (x2 + y2) / (y3 - 2xy)?

## Fundamentals

The Calculus
Calculus is a branch of mathematics which uses derivative to analyze the way in which the values of a function vary. Developed on 17th century, Calculus has now applications almost in all areas of human endeavor: engineering, physics, business, economics, astronomy, chemistry, biology, psychology, sociology, etc. Sir Isaac Newton (1642 – 1727) and Gottfried Wilhelm Leibniz (1646 – 1716), working independently from each other, developed the Calculus in connections with their work. Newton used Calculus in finding the velocity of a moving body, the work done by force and the centroid of mass of a body. Leibniz on the other hand focused on geometric calculation like finding the tangent and normal to a curve, area bounded by two or more curves, and volume of a solid. Leibniz is the one who initiated the modern notation of dx and $\displaystyle \int$.

## The Circle

The following are short descriptions of the circle shown below.

Tangent
Tangent is a line that would pass through one point on the circle.
Secant
Secant is a line that would pass through two points on the circle.
Chord
Chord is a secant that would terminate on the circle itself.
Diameter, d
Diameter is a chord that passes through the center of the circle. 