1, cartesian coordinate equation.

The expression of the plane rectangular coordinate system equation of the heart-shaped line is:

x^2+y^2+a*x=a*sqrt(x^2+y^2)； x^2+y^2-a*x=a*sqrt(x^2+y^2)。

2. Polar coordinate equation.

Horizontal direction: ρ=a( 1-cosθ) or ρ = a (1+cos θ) (a > 0); Vertical direction: ρ=a( 1-sinθ) or ρ = a (1+sinθ) (a > 0)。

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Rene descartes (rene descartes,1March 3, 5961-1February 0650+0, 65438),1March 3, 5961was born in Dulan (now Descartes). He made an important contribution to the development of modern mathematics, and was known as the father of analytic geometry because he formulated the geometric coordinate system.

He is also one of the founders of modern western philosophy and a pioneer of modern materialism, and put forward the idea of "universal doubt". His philosophical thoughts deeply influenced later generations of Europeans and laid the foundation of European rationalism philosophy. Descartes' achievements as a mathematician are best known. 1637, he invented the coordinate system, one of the basic tools of modern mathematics, and combined geometry with algebra to create analytic geometry. At the same time, he also derived geometric formulas such as Descartes theorem. It is worth mentioning that the legendary famous heart-shaped equation was also put forward by Descartes.

In philosophy, Descartes is a dualist and a rationalist. He is a pioneer of European rationalism. Regarding Descartes' philosophical thoughts, the most famous one is his sentence "I think, therefore I am?" . His Meditations on the First Philosophy (also called Metaphysical Meditations) is still one of the required books for many university philosophy departments.

In physics, Descartes applied his coordinate geometry to the study of optics, and proved the law of refraction in theory for the first time in Refractive Optics. In the second chapter of his Principles of Philosophy, the law of inertia is completely expressed in the form of the first law and the second law of nature for the first time, and the law of conservation of momentum is clearly put forward for the first time. All these laid a certain foundation for the later research of Newton and others.