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Joint Entrance Examination
Mathematics
Straight Lines and Pair of Straight Lines
Question 238
Question 238 of 303
Medium
MCQ
If
x
1
,
x
2
,
x
3
x_1,x_2,x_3
x
1
,
x
2
,
x
3
and
y
1
,
y
2
,
y
3
y_1,y_2,y_3
y
1
,
y
2
,
y
3
are both in G.P. with the same common ratio, then the points
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
(x_1,y_1),(x_2,y_2)
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
and
(
x
3
,
y
3
)
(x_3,y_3)
(
x
3
,
y
3
)
:
A
are vertices of a triangle
B
lie on a straight line
C
lie on an ellipse
D
lie on a circle.
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Solutions · 1
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Official solution
Taking co-ordinates as \[\left( {{x \over r},{y \over r}} \right);\left( {x,y} \right)\,\,\& \,\,\left( {xr,yr} \right)\] Then slope of line joining \[\left( {{x \over r},{y \over r}} \right),\left( {x,y} \right) = {{y\left( {1 - {1 \over r}} \right)} \over {x\left( {1 - {1 \over r}} \right)}} = {y \over x}\] and slope of line joining
(
x
,
y
)
(x,y)
(
x
,
y
)
and
(
x
r
,
y
r
)
(xr, yr)
(
x
r
,
y
r
)
\[ = {{y\left( {r - 1} \right)} \over {x\left( {r - 1} \right)}} = {y \over x}\] \[\therefore\]
m
1
=
m
2
{m_1} = {m_2}
m
1
=
m
2
\[ \Rightarrow \] Points lie on the straight line.
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