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Byju's Answer
Standard XII
Mathematics
Axis
For parabola ...
Question
For parabola
y
2
=
84
x
, end points of latus rectum and length of L.R. is
A
(
0
,
21
)
,
84
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B
(
21
,
±
42
)
,
84
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C
(
0
,
±
21
)
,
42
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D
(
±
21
,
42
)
,
21
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Solution
The correct option is
D
(
21
,
±
42
)
,
84
For the parabola
(
y
−
k
)
2
=
4
a
(
x
−
h
)
,
end points of latus rectum are
(
h
+
a
,
k
+
2
a
)
and
(
h
+
a
,
k
−
2
a
)
and length of latus rectum
=
4
a
For the given parabola
y
2
=
84
x
=
4
(
21
)
x
h
=
k
=
0
and
a
=
21
So, end points of latus rectum are
(
21
,
42
)
and
(
21
,
−
42
)
and length of latus rectum
=
84
So, the answer is option (B).
Suggest Corrections
0
Similar questions
Q.
Find the coordinate of focus, equation of directrix, length of latus Rectum and coordinate of end point of latus rectum for the parabola.
y
2
=
20
x
.
Q.
Let a circle
x
2
+
y
2
−
2
x
−
3
=
0
touches the directrix of a parabola and passes through end points of latus rectum of the same parabola. If latus rectum of the parabola is chord of maximum length with respect to given circle and equation of parabola is
y
2
=
k
x
, then
k
=
Q.
Let
P
(
x
1
,
y
1
)
and
Q
(
x
2
,
y
2
)
,
y
1
<
0
,
y
2
<
0
, be the end points of the latus rectum of the ellipse
x
2
+
4
y
2
=
4
. The equations of parabolas with latus rectum
P
Q
are
Q.
P
(
x
1
,
y
1
)
and
Q
(
x
2
,
y
2
)
,
y
1
<
0
,
y
2
<
0
are the end points of the latus rectum of the ellipse
x
2
+
4
y
2
=
4
. The equations of the parabolas with latus rectum
P
Q
are
Q.
Let
P
(
x
1
,
y
1
)
and
Q
(
x
2
,
y
2
)
;
where
y
1
<
0
,
y
2
<
0
be the end points of the latus rectum of the ellipse
x
2
+
4
y
2
=
4.
The equation of parabola with latus rectum
P
Q
are
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