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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1964 AMC 12/AHSME
15
15
Part of
1964 AMC 12/AHSME
Problems
(1)
Line Cutting From Second Quadrant
Source: 1964 AHSME #15
10/20/2012
A line through the point
(
−
a
,
0
)
(-a,0)
(
−
a
,
0
)
cuts from the second quadrant a triangular region with area
T
T
T
. The equation of the line is:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
2
T
x
+
a
2
y
+
2
a
T
=
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
2
T
x
−
a
2
y
+
2
a
T
=
0
<span class='latex-bold'>(A)</span>\ 2Tx+a^2y+2aT=0 \qquad<span class='latex-bold'>(B)</span>\ 2Tx-a^2y+2aT=0 \qquad
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
2
T
x
+
a
2
y
+
2
a
T
=
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
2
T
x
−
a
2
y
+
2
a
T
=
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
2
T
x
+
a
2
y
−
2
a
T
=
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
2
T
x
−
a
2
y
−
2
a
T
=
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
none of these
{{<span class='latex-bold'>(C)</span>\ 2Tx+a^2y-2aT=0 \qquad<span class='latex-bold'>(D)</span>\ 2Tx-a^2y-2aT=0 }\qquad<span class='latex-bold'>(E)</span>\ \text{none of these} }
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
2
T
x
+
a
2
y
−
2
a
T
=
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
2
T
x
−
a
2
y
−
2
a
T
=
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
none of these
geometry
AMC