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Byju's Answer
Standard XII
Mathematics
Obtaining Centre and Radius of a Circle from General Equation of a Circle
If the centre...
Question
If the centre of the circle inscribed in square formed by the lines
x
2
−
8
x
+
12
=
0
and
y
2
−
14
y
+
45
=
0
is
(
a
,
b
)
,
then the value of
a
+
b
is
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Solution
We have,
x
2
−
8
x
+
12
=
0
⇒
(
x
−
6
)
(
x
−
2
)
=
0
and,
y
2
−
14
y
+
45
=
0
⇒
(
y
−
5
)
(
y
−
9
)
=
0
Thus, sides of square are
x
=
2
,
x
=
6
,
y
=
5
,
y
=
9
∴
Centre of the circle inscribed in square is
(
2
+
6
2
,
5
+
9
2
)
=
(
4
,
7
)
∴
a
+
b
=
4
+
7
=
11
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