Find the equation of the parabola whose vertex is at (2 1) and the directrix is x=y-1
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Given -
Vertex
(
−
2
,
1
)
Directrix
x
=
1
The vertex is in the 2nd quadrant. The directrix is parallel to the y-axis. So, the parabola opens to the left. The vertex of the parabola is not the origin. Then its general form is -
(
y
−
k
)
2
=
−
4
.
a
.
(
x
−
h
)
Where -
h
and
k
are the coordinates of the vertex.
h
=
−
2
)
k
=
1
a
=
1.5
half the distance between Directrix and vertex [= distance between focus and vertex]
Substitute these values in the equation
(
y
−
1
)
2
=
−
4.1
.5
.
(
x
+
2
)
y
2
−
2
y
+
1
=
−
6
x
−
12
−
6
x
−
12
=
y
2
−
2
y
+
1
−
6
x
=
y
2
−
2
y
+
1
+
12
x
=
y
2
−
6
−
2
y
−
6
+
13
−
6
x
=
−
y
2
6
+
y
3
−
13
6
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