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KEAM 2017 Math Paper
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© examsnet.com
Question : 13
Total: 120
The centre of the ellipse
4
x
2
+
y
2
–
8
x
+
4
y
–
8
=
0
is
(0, 2)
(2, – 1)
(2, 1)
(1, 2)
(1, – 2)
Validate
Solution:
We have
4
x
2
+
y
2
−
8
x
+
4
y
−
8
=
0
⇒
(
4
x
2
−
8
x
)
+
(
y
2
+
4
y
)
−
8
=
0
⇒
4
(
x
2
−
2
x
)
+
(
y
2
+
4
y
)
−
8
=
0
⇒
4
[
(
x
−
1
)
2
−
1
]
+
[
(
y
+
2
)
2
−
4
]
−
8
=
0
⇒
4
(
x
−
1
)
2
−
4
+
(
y
+
2
)
2
−
4
−
8
=
0
⇒
4
(
x
−
1
)
2
+
(
y
+
2
)
2
=
16
⇒
(
x
−
1
)
2
4
+
(
y
+
2
)
2
16
=
1
∴
Centre
=
(
1
,
−
2
)
© examsnet.com
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