1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Representation of Solutions on a Number Line
Write the cen...
Question
Write the centre and eccentricity of the ellipse 3x
2
+ 4y
2
− 6x + 8y − 5 = 0.
Open in App
Solution
3
x
2
-
6
x
+
4
y
2
+
8
y
-
5
=
0
⇒
3
(
x
2
-
2
x
)
+
4
(
y
2
+
2
y
)
=
5
⇒
3
(
x
2
-
2
x
+
1
)
+
4
(
y
2
+
2
y
+
1
)
=
5
+
3
+
4
⇒
3
(
x
-
1
)
2
+
4
(
y
+
1
)
2
=
12
⇒
3
(
x
-
1
)
2
12
+
4
(
y
+
1
)
2
12
=
1
⇒
(
x
-
1
)
2
4
+
(
y
+
1
)
2
3
=
1
Compairing
it
with
x
2
a
2
+
y
2
b
2
=
1
,
we
get
:
a
=
2
and
b
=
3
Here
,
a
>
b
,
so
the
major
and
t
h
e
minor
ax
e
s
of
the
ellipse
are
along
the
x
-
axis
and
y
-
ax
i
s
,
respectively
.
Now
,
e
=
1
-
b
2
a
2
⇒
e
=
1
-
3
4
⇒
e
=
1
4
∴
e
=
1
2
and centre =
1
,
-
1
Suggest Corrections
0
Similar questions
Q.
The eccentricity of the ellipse
x
2
+
4
y
2
+
8
y
−
2
x
+
1
=
0
is
Q.
Foci of the ellipse
3
x
2
+
4
y
2
−
12
x
−
8
y
+
4
=
0
are:
Q.
Directrices of the ellipse
3
x
2
+
4
y
2
+
12
x
−
8
y
−
32
=
0
are:
Q.
The eccentricity of an ellipse, with its centre at the origin, is
1
2
. If one of the directrices is x = 4, then the equation of the ellipse is
Q.
Find the eccentricity, foci and the length of the latus-rectum of the ellipse
x
2
+
4
y
2
+
8
y
−
2
x
+
1
=
0
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Representation of Solutions on a Number line
MATHEMATICS
Watch in App
Explore more
Representation of Solutions on a Number Line
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app