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Byju's Answer
Standard XII
Mathematics
Parabola
Ends of latus...
Question
Ends of latus rectum of a parabola are
−
3
,
1
and
1
,
1
, then one of the equation of the parabola is
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Solution
Mid point of Latus Rectum gives Focus of Parabola which is
(
−
2
,
1
)
Lentgh of latus rectum is
4
a
⟹
a
=
1
Slope of latus rectum is
1
−
1
1
+
3
=
0
Axis is perpendicular to latus rectum so Slope of Axis is
∞
i.e., parallel to
Y
−
a
x
i
s
and passes through
(
−
2
,
1
)
So equation of Axis is
x
=
−
2
Vertices are
(
2
,
0
)
or
(
2
,
2
)
considering
(
2
,
0
)
General form of equation is
(
x
−
h
)
2
=
4
a
(
y
−
k
)
⟹
(
x
−
2
)
2
=
4
(
1
)
(
y
)
⟹
x
2
−
2
x
+
4
=
4
y
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