To understand the standard equation of a circle, we need to understand the concept of square first. Square refers to a number multiplied by itself, such as 2 2 = 4, (3) 2 = 9. In the standard equation of a circle, (X-A) 2 represents the square of the difference between the X coordinate and the central coordinate A, and (Y-B) 2 represents the square of the difference between the Y coordinate and the central coordinate B. ..
The standard equation formula of a circle means that for any point P(x, y) on the circle, the square of the distance from p to the center (a, b) is equal to R 2. That is, (x-a) 2+(y-b) 2 = r 2.
This formula is widely used, for example, in geometry, we can use it to describe the position and size of circular objects; In physics, we can use it to describe the propagation of electromagnetic waves; In engineering, we can use it to describe the shape and size of mechanical parts.
The standard equation formula of circle can not only help us accurately describe the position and size of circular objects, but also help us solve some problems related to circular objects.
Common formulas about circles:
1, the circumference formula of a circle: C=2πr, where r is the radius of the circle and π is a mathematical constant, which is about equal to 3. 14 159.
2. Formula of circle area: S=πr? Where r is the radius of a circle and π is a mathematical constant, which is approximately equal to 3. 14 159.
3. Standard equation of circle: (x-a)? +(y-b)？ =r？ , where (a, b) is the coordinate of the center of the circle and r is the radius of the circle.
4. General equation of circle: x? +y？ +Dx+Ey+F=0, where d, e and f are constants and represent a circle.
5. The tangent equation of the circle: For the circle (x-a)? +(y-b)？ =r？ The tangent equation can be expressed as: (x-a)(x-a0)+(y-b)(y-b0)=r? , where (a0, b0) is the coordinates of the tangent point.