Question

下列哪一项描述方程 $(x + y)^2 = x^2 + y^2$ 的图形？

Which of the following describes the graph of the equation $(x + y)^2 = x^2 + y^2?$

空集

the empty set

一个点

one point

两条直线

two lines

一个圆

a circle

整个平面

the entire plane

展开得 $x^2 + 2xy + y^2 = x^2 + y^2$ ，所以 $2xy = 0$ ，即 $xy = 0$ 。

这是两条坐标轴的并集，也就是一对直线。

因此，正确答案是 C。

Expanding, $x^2 + 2xy + y^2 = x^2 + y^2,$ so $2xy = 0,$ i.e. $xy = 0.$

This is the union of the two coordinate axes, a pair of lines.

Thus, the correct answer is C.