题目

Problem

A circle has equation $(x - 1)^2 + (y + 4)^2 = 40$ . A line with equation $y = x - 9$ intersects the circle at points $A$ and $B$ .

(a) Find the coordinates of the two points of intersection.

[4]

(b) Find an equation of the circle with diameter $AB$ .

[3]

题目中文翻译

一个圆的方程为 $(x - 1)^2 + (y + 4)^2 = 40$ 。方程为 $y = x - 9$ 的直线与该圆相交于点 $A$ 和 $B$ 。

(a) 求两个交点的坐标。

[4]

(b) 求以 $AB$ 为直径的圆的方程。

[3]

CIE 9709 2023 June Paper 13 Q5