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Mathematics
Let x2=3ax+2ay+3 is a family of parabola where a is parameter. Then the locus of the vertex of the parabola is
Q. Let
x
2
=
3
a
x
+
2
a
y
+
3
is a family of parabola where
a
is parameter. Then the locus of the vertex of the parabola is
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NTA Abhyas 2022
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A
3
x
2
+
4
x
y
+
9
=
0
B
4
x
2
+
3
x
y
+
9
=
0
C
4
x
2
+
9
x
y
+
3
=
0
D
none of these
Solution:
Given equation of parabola
x
2
=
3
a
x
+
2
a
y
+
3
where a is variable on solving
(
x
−
2
3
a
)
2
=
2
a
(
y
+
8
a
12
+
9
a
2
)
,
, vertex
v
(
2
3
a
,
−
8
a
(
12
+
9
a
2
)
)
Let
v
(
h
,
k
)
h
=
2
3
a
,
k
=
−
8
a
(
12
+
9
a
2
)
3
h
2
+
4
hk
+
9
=
0
So, locus is
3
x
2
+
4
x
y
+
9
=
0