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Mathematics
Mathematics
Problem
Consider the equation
x
2
+
y
2
+
2
k
x
−
4
y
+
(
k
2
−
5
)
=
0
x^2 + y^2 + 2kx - 4y + (k^2 - 5) = 0
x
2
+
y
2
+
2
k
x
−
4
y
+
(
k
2
−
5
)
=
0
, where
k
k
k
is a real parameter. a. (i) Find the range of
k
k
k
for which this equation represents a real circle. b. (ii) For
k
=
3
k = 3
k
=
3
, calculate the radius of the circle.
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