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Find the equation of parabola whose vertex is (-1,1) and directrix is 4x+3y-24=0
Answers
Answer:
Length of latus rectum is twice the distance between focus and vertex or four times the distance of focus from directrix.
The distance of focus
(
−
1
,
1
)
from directrix
4
x
+
3
y
−
24
=
0
is
∣
∣
∣
∣
4
×
(
−
1
)
+
3
×
1
−
24
√
4
2
+
3
2
∣
∣
∣
∣
=
∣
∣
∣
−
4
+
3
−
24
5
∣
∣
∣
=
∣
∣
∣
−
25
5
∣
∣
∣
=
5
Hence, length of latus rectum is
10
.
As parabola is locus of a point, which moves so that its distance from focus and directrix is alwaays equal, its equation is
∣
∣
∣
∣
4
x
+
3
y
−
24
√
4
2
+
3
2
∣
∣
∣
∣
2
=
(
x
+
1
)
2
+
(
y
−
1
)
2
or
16
x
2
+
9
y
2
+
576
+
24
x
y
−
192
x
−
144
y
=
25
x
2
+
50
x
+
25
+
25
y
2
−
50
y
+
25
or
9
x
2
+
16
y
2
−
24
x
y
+
242
x
+
94
y
−
526
=
0
Ends of latus rectum are
(
−
4
,
5
)
and
(
2
,
−
3
)
graph{(9x^2+16y^2-24xy+242x+94y-526)((x+1)^2+(y-1)^2-0.08)((x+4)^2+(y-5)^2-0.08)((x-2)^2+(y+3)^2-0.08)(4x+3y-24)(4x+3y+1)=0 [-10.42, 9.58, -4.16, 5.84]}
Answer:
10 is the correct answer
Step-by-step explanation: