1964 AMC 12 Problem 15

Attempt Problem 15 of the 1964 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 1964 AMC 12 solutions, or check the answer key.

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15.

A line through the point

(-a,0)

cuts from the second quadrant a triangular region with area

T.

The equation of the line is:

2Tx+a^2y+2aT=0

2Tx-a^2y+2aT=0

2Tx+a^2y-2aT=0

2Tx-a^2y-2aT=0

none of these

If the positive

y

-intercept is

b,

then

\frac12ab=T

Use the intercept form

-\frac{x}{a}+\frac{y}{b}=1

Let the

y

-intercept be

b.

The second-quadrant triangle has area

\frac{ab}{2}=T,

b=\frac{2T}{a}.

The intercept form is

\frac{x}{-a}+\frac{y}{\frac{2T}{a}}=1.

Clearing denominators gives

2Tx-a^2y+2aT=0.

Therefore, the correct answer is B.

Problem 15 in other years