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Mathematics
Mathematics
Problem
The values of
λ
\lambda
λ
for which the circle
x
2
+
y
2
+
6
x
+
5
+
λ
(
x
2
+
y
2
−
8
x
+
7
)
=
0
x^2 + y^2 + 6x + 5 + \lambda(x^2 + y^2 - 8x + 7) = 0
x
2
+
y
2
+
6
x
+
5
+
λ
(
x
2
+
y
2
−
8
x
+
7
)
=
0
dwindles into a point are a.
1
±
2
3
1 \pm \frac{\sqrt{2}}{3}
1
±
3
2
b.
2
±
2
2
3
2 \pm \frac{2\sqrt{2}}{3}
2
±
3
2
2
c.
2
±
4
2
3
2 \pm \frac{4\sqrt{2}}{3}
2
±
3
4
2
d.
1
±
4
2
3
1 \pm \frac{4\sqrt{2}}{3}
1
±
3
4
2
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