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Byju's Answer
Standard XII
Mathematics
Latus Rectum
If the line ...
Question
If the line
l
x
+
m
y
+
n
=
0
touches the parabola
y
2
=
4
a
x
, then
l
n
=
A
l
n
=
a
m
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B
l
n
=
a
m
2
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C
l
n
=
1
2
a
m
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D
l
n
=
a
m
3
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Solution
The correct option is
B
l
n
=
a
m
2
The x-coordinates of the points of intersection of the line
l
x
+
m
y
+
n
=
0
or
y
=
−
(
l
x
+
n
m
)
and the parabola
y
2
=
4
a
x
are roots of the equation.
[
−
(
l
x
+
n
m
)
]
2
=
4
a
x
l
2
x
2
+
2
x
(
l
n
−
2
a
m
2
)
+
n
2
=
0
If the line
l
x
+
m
y
+
n
=
0
touches the parabola
y
2
=
4
a
x
, then this equation has equal roots.
Therefore,
4
(
l
n
−
2
a
m
2
)
2
−
4
l
2
n
2
=
0
−
4
a
l
m
2
n
+
4
a
2
m
4
=
0
l
n
=
a
m
2
Suggest Corrections
0
Similar questions
Q.
If the line
l
x
+
m
y
+
n
=
0
touches the parabola
y
2
=
4
a
x
, prove that
l
n
=
a
m
2
.
Q.
Prove that the straight line Ix + my + n = 0 touches the parabola
y
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a
x
if
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n
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2
.
Q.
The condition that the straight line
l
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m
y
+
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=
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touches the parabola
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=
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Q.
The condition so that the line
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=
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may touch the parabola
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Q.
If
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.
.
.
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are in G.P., then the value of the determinant
∣
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a
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ln
a
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+
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4
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+
5
ln
a
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+
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ln
a
n
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7
ln
a
n
+
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∣
∣ ∣
∣
is
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