1955 AMC 12 Problem 8

Attempt Problem 8 of the 1955 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1955 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The graph of

x^2-4y^2=0:

is a hyperbola intersecting only the

x

-axis

is a hyperbola intersecting only the

y

-axis

is a hyperbola intersecting neither axis

is a pair of straight lines

does not exist

Factor the difference of squares

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

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.

Problem 8 in other years