Question

The lines represented by 5x+3y-7=0 and 6y +10x -14 =0 are ?

Answer 1

centre :
C
(
5
,
−
3
)

radius :
r
=
4
Explanation:
The general equation of a circle:
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
...
...
...
.
.
→
(
1
)
,
whose centre is
C
(
−
g
−
f
)
and radius is
r
=
√
g
2
+
f
2
−
c
We have,
x
2
+
y
2
−
10
x
+
6
y
+
18
=
0
Comparing with
e
q
u
n
(
1
)
, we get
2
g
=
−
10
,
2
f
=
6
and
c
=
18
⇒
g
=
−
5
,
f
=
3
and
c
=
18
So,
radius
r
=
√
(
−
5
)
2
+
(
3
)
2
−
18
=
√
25
+
9
−
18
=
√
16
=
4
i.e.
r
=
4
>
0
centre
C
(
−
g
,
−
f
)
⇒
C
(
−
(
−
5
)
,
−
3
)
i.e. centre
C
(
5
,
−
3
)