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Mathematics
Mathematics
Problem
The circle
x
2
+
y
2
=
4
x^2 + y^2 = 4
x
2
+
y
2
=
4
cuts the line joining the points
A
(
1
,
0
)
A(1, 0)
A
(
1
,
0
)
and
B
(
3
,
4
)
B(3, 4)
B
(
3
,
4
)
in two points
P
P
P
and
Q
Q
Q
. Let
B
P
P
A
=
α
\frac{BP}{PA} = \alpha
P
A
B
P
=
α
and
B
Q
Q
A
=
β
\frac{BQ}{QA} = \beta
Q
A
B
Q
=
β
, then
α
\alpha
α
and
β
\beta
β
are roots of the quadratic equation a.
x
2
+
2
x
+
7
=
0
x^2 + 2x + 7 = 0
x
2
+
2
x
+
7
=
0
b.
3
x
2
+
2
x
−
21
=
0
3x^2 + 2x - 21 = 0
3
x
2
+
2
x
−
21
=
0
c.
2
x
2
+
3
x
−
27
=
0
2x^2 + 3x - 27 = 0
2
x
2
+
3
x
−
27
=
0
d. None of these
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