Question

圆心在直线2x-y-7=0上的圆C与y轴交于两点A(0,-4)、B(0,-2),则圆C的方程为_______.

Answer 1

答案：（x-2)²+(y+3)²=5

解析：设圆C的方程为(x-x₀)²+(y-y₀)²=r².

∵圆心在直线2x-y-7=0上，

∴2x₀-y₀-7=0.                                                                 ①

又∵圆过A（0,-4）、B(0,-2),

∴x₀²+(-4-y₀)²=r²,                                                             ②

x₀²+(-2-y₀)²=r².                                                               ③

由①②③解得

∴圆的方程为(x-2)²+(y+3)²=5.