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Byju's Answer
Standard XII
Mathematics
Obtaining Centre and Radius of a Circle from General Equation of a Circle
For what valu...
Question
For what value of
k
the circles
x
2
+
y
2
+
5
x
+
3
y
+
7
=
0
and
x
2
+
y
2
−
8
x
+
6
y
+
k
=
0
cut orthogonally.
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Solution
We have,
x
2
+
y
2
+
5
x
+
3
y
+
7
=
0
.
.
.
.
.
.
.
.
.
.
.
(
1
)
x
2
+
y
2
−
8
x
+
6
y
+
k
=
0
.
.
.
.
.
.
.
.
.
.
.
.
(
2
)
We know that the condition of two circles are orthogonal
2
g
1
g
2
+
2
f
1
f
2
=
c
1
+
c
2
Therefore,
2
(
5
2
)
(
−
4
)
+
2
(
3
2
)
(
3
)
=
7
+
k
−
20
+
9
=
7
+
k
k
=
−
18
Hence, this is the answer.
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0
Similar questions
Q.
Match the following
I
: lf
x
2
+
y
2
−
6
x
−
8
y
+
12
=
0
,
a
)
2
x
2
+
y
2
−
4
x
+
6
y
+
k
=
0
cut orthogonally then
k
=
I
I
lf
x
2
+
y
2
−
2
x
+
3
y
+
k
=
0
,
b
)
−
10
x
2
+
y
2
+
8
x
−
6
y
−
7
=
0
cut orthogonally then
k
=
I
I
I
: lf
x
2
+
y
2
+
2
x
−
2
y
+
4
=
0
,
c
)
−
24
x
2
+
y
2
+
4
x
−
2
y
+
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=
0
cut orthogonally then
k
=
Q.
A
: If
x
2
+
y
2
−
2
x
+
3
y
+
k
=
0
and
x
2
+
y
2
+
8
x
−
6
y
−
7
=
0
cut each other orthogonally, then
k
=
10
R
:
The circles
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
and
x
2
+
y
2
+
2
g
′
x
+
2
f
′
y
+
c
′
=
0
cut each other orthogonally if
2
g
g
′
+
2
f
f
′
=
c
+
c
′
Q.
If the two circles
2
x
2
+
2
y
2
−
3
x
+
6
y
+
k
=
0
and
x
2
+
y
2
−
4
x
+
10
y
+
16
=
0
cut orthogonally, then the value of
k
is .
Q.
If the circle
x
2
+
y
2
+
8
x
−
4
y
+
c
=
0
touches the circle
x
2
+
y
2
+
2
x
+
4
y
−
11
=
0
externally and cuts the circle
x
2
+
y
2
−
6
x
+
8
y
+
k
=
0
orthogonally then
k
=
Q.
The two circles
x
2
+
y
2
−
2
x
+
22
y
+
5
=
0
and
x
2
+
y
2
+
14
x
+
6
y
+
k
=
0
intersect orthogonally provided
k
is equal to ?
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