What is the equation for the parabola that
has a focus at (-7, 6) and a directrix of x
1?
1 answer:
Answer:
Step-by-step explanation:
Parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
Explanation:
Parabola is locus of a point which moves so that its distance from a given point calld focus and a given line ccalled directrix is always constant.
Let the point be
(
x
,
y
)
. Here focus is
(
7
,
5
)
and distance from focus is
√
(
x
−
7
)
2
+
(
y
−
5
)
2
. Its distance from directrix
y
=
−
3
i.e.
y
+
3
=
0
is
|
y
+
3
|
.
Hence equaion of parabola is
(
x
−
7
)
2
+
(
y
−
5
)
2
)
=
|
y
+
3
|
2
or
x
2
−
14
x
+
49
+
y
2
−
10
y
+
25
=
y
2
+
6
y
+
9
or
x
2
−
14
x
+
65
=
16
y
i.e.
y
=
1
16
(
x
2
−
14
x
+
49
−
49
)
+
65
16
or
y
=
1
16
(
x
−
7
)
2
+
65
−
49
16
or
y
=
1
16
(
x
−
7
)
2
+
1
Hence parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
graph{(1/16(x-7)^2+1-y)((x-7)^2+(y-1)^2-0.15)((x-7)^2+(y-5)^2-0.15)(y+3)=0 [-12.08, 27.92, -7.36, 12.64]}
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