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Byju's Answer
Standard XII
Mathematics
General Equation of Parabola
Find vertex a...
Question
Find vertex and focus for the equation
y
2
−
8
y
−
x
+
19
=
0
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Solution
y
2
−
8
y
−
x
+
19
=
0
y
2
−
2
(
4
)
y
+
16
+
3
=
x
(
y
−
4
)
2
=
(
x
−
3
)
[
y
2
=
4
a
x
A
=
1
4
]
y
=
y
−
4
x
=
x
−
3
x
=
3
y
=
4
v
e
r
t
e
x
=
(
3
,
4
)
f
o
c
u
s
:
x
−
3
=
1
4
x
=
13
4
y
=
4
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Similar questions
Q.
Find the vertex, focus, axis, latusrectum of the parabolas reducible to the standard form.
y
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8
y
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x
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19
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Q.
Find the vertex focus, equation of directrix and equation of axis of the
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.
Q.
The equation of the parabola with focus (0, 0) and directrix x + y = 4 is
(a) x
2
+ y
2
− 2xy + 8x + 8y − 16 = 0
(b) x
2
+ y
2
− 2xy + 8x + 8y = 0
(c) x
2
+ y
2
+ 8x + 8y − 16 = 0
(d) x
2
− y
2
+ 8x + 8y − 16 = 0