Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If the circles
x
2
+
y
2
+
2
a
x
+
c
y
+
a
=
0
x^2 + y^2 + 2ax + cy + a = 0
x
2
+
y
2
+
2
a
x
+
cy
+
a
=
0
and
x
2
+
y
2
−
3
a
x
+
d
y
−
1
=
0
x^2 + y^2 - 3ax + dy - 1 = 0
x
2
+
y
2
−
3
a
x
+
d
y
−
1
=
0
intersect in two distinct points
P
P
P
and
Q
Q
Q
, then the line
5
x
+
b
y
−
a
=
0
5x + by - a = 0
5
x
+
b
y
−
a
=
0
passes through
P
P
P
and
Q
Q
Q
. a. exactly one value of
a
a
a
b. no value of
a
a
a
c. infinitely many values of
a
a
a
d. exactly two values of
a
a
a
Browse the problem library