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Question
Mathematics
If the equation of circle is x2+y2+8 x+10 y-8=0, then I. The centre is (-4,-5). II. The radius is 7.
Q. If the equation of circle is
x
2
+
y
2
+
8
x
+
10
y
−
8
=
0
, then
I. The centre is
(
−
4
,
−
5
)
.
II. The radius is 7.
147
142
Conic Sections
Report Error
A
Both I and II are true
42%
B
Only I is true
32%
C
Only II is true
15%
D
Both I and II are false
11%
Solution:
The given equation is
(
x
2
+
8
x
)
+
(
y
2
+
10
y
)
=
8
Now, completing the squares within the parenthesis, we get
(
x
2
+
8
x
+
16
)
+
(
y
2
+
10
y
+
25
)
=
8
+
16
+
25
i.e.
(
x
+
4
)
2
+
(
y
+
5
)
2
=
49
i.e.
{
x
−
(
−
4
)
}
2
+
{
y
−
(
−
5
)
}
2
=
7
2
Therefore, the given circle has centre at
(
−
4
,
−
5
)
and radius 7 .