Q.5) find the center and radius of the equation: x² + y² - 2x + 4y - 4 =0
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Answer:
centre =(1 , -2 ) and r = 3
Step-by-step explanation:
The general equation of a circle is
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
the equation here
x
2
+
y
2
−
2
x
+
4
y
−
4
=
0
is in this form and by comparison of the 2 equations , obtain
2g = - 2 → g = -1 and 2f = 4 → f = 2 , c = -4
now centre = (-g , -f ) = (1 , -2 )
and radius , r
=
√
g
2
+
f
2
−
c
hence r
=
√
(
−
1
)
2
+
2
2
+
4
=
√
9
=
3
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