1955 AMC 12 第 8 题

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.

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