The equation of line and circle in high school mathematics In a triangle, the opposite sides of angle a, angle B and angle c are known to be a, B and C respectively, and a > C > b is an arithmetic sequence, | ab | = 2. The trajectory equation of the vertex is obtained

The equation of line and circle in high school mathematics In a triangle, the opposite sides of angle a, angle B and angle c are known to be a, B and C respectively, and a > C > b is an arithmetic sequence, | ab | = 2. The trajectory equation of the vertex is obtained

a. C. B is a sequence of arithmetic numbers, a + B = 2C
∵ C = 2, | a + B = 4, that is | Ca | + | CB | = 4
So the trajectory of point C is an ellipse with a and B as focal lengths
∵2a=4 2c=2,∴a=2 c=1,∴b²=4-1=3
The elliptic equation is X & # 178 / 4 + Y & # 178 / 3 = 1