Question

方程 $x^2-4y^2=0$ 的图形：

The graph of $x^2-4y^2=0:$

是只与 $x$ 轴相交的双曲线

is a hyperbola intersecting only the $x$ -axis

是只与 $y$ 轴相交的双曲线

is a hyperbola intersecting only the $y$ -axis

是与两条坐标轴都不相交的双曲线

is a hyperbola intersecting neither axis

是一对直线

is a pair of straight lines

不存在

does not exist

将平方差因式分解

Factor the difference of squares

两个一次因式的乘积为零时，至少有一个因式为零

A product is zero when at least one of its two linear factors is zero

因式分解得 $x^2-4y^2=(x-2y)(x+2y)\text{。}$ 因此图形是直线 $x=2y$ 与 $x=-2y$ 的并集。

正确答案是 D。

Factoring, $x^2-4y^2=(x-2y)(x+2y).$ Thus the graph is the union of the two straight lines $x=2y$ and $x=-2y.$

The correct answer is D.