Math Problem Statement

Escribir la ecuación general de la circunferencia, que pasa por tres puntos conocidos: (0, 0), (3, 1), (5, 7).

Solution

La ecuación general de la circunferencia es:

x2+y2+Dx+Ey+F=0x^2 + y^2 + Dx + Ey + F = 0

Para determinar D,E,FD, E, F, se sustituyen las coordenadas de los tres puntos dados en la ecuación y se resuelve el sistema de ecuaciones resultante.

¿Sobre qué conjunto de puntos deseas que calcule la ecuación de la circunferencia?

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Analytic Geometry
Systems of Linear Equations
Circumference Equation

Formulas

General equation of a circle: x^2 + y^2 + Dx + Ey + F = 0
Substitution of points to form equations: x_i^2 + y_i^2 + Dx_i + Ey_i + F = 0
Solving systems of linear equations to find D, E, F

Theorems

General properties of a circle in the Cartesian plane

Suitable Grade Level

Grades 10-12

Related Recommendation

Equation of a Circle Passing Through Three Points (5,7), (8,1), and (1,3)

Find the Equation of a Circle Passing Through Three Points

Equation of a Circle Passing Through Three Points (2,3), (3,4), (-1,2)

Find the Equation of a Circle Passing Through Three Points: (2, -2), (5, 3), (8, 4)

Find the Equation of a Circle Passing Through Three Points: (-3,6), (-5,2), and (3,-6)