Find the centre and radius of the circle x^2 - 3x + y^2 = 0
Answers
⇒x
2
+2×
2
3
x+
4
9
−
4
9
+y
2
+2×
2
5
y+
4
25
−
4
25
+11=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
4
9
−
4
25
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
4
9+25
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
4
34
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
2
17
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
=
2
17
which is comparable with (x−h)
2
+(y−k)
2
=r
2
where h=
2
−3
,k=
2
−5
and r=
2
17
Hence, the given circle has centre (
2
−3
, ⇒x
2
+2×
2
3
x+
4
9
−
4
9
+y
2
+2×
2
5
y+
4
25
−
4
25
+11=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
4
9
−
4
25
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
4
9+25
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
4
34
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
−
2
17
=0
⇒(x+
2
3
)
2
+(y+
2
5
)
2
=
2
17
which is comparable with (x−h)
2
+(y−k)
2
=r
2
where h=
2
−3
,k=
2
−5
and r=
2
17
Hence, the given circle has centre (
2
−3
,
2
−5
) and its radius=
2
17
2
−5
) and its radius=
2
17