Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Consider a curve
a
x
2
+
2
h
x
y
+
b
y
2
=
1
ax^2 + 2hxy + by^2 = 1
a
x
2
+
2
h
x
y
+
b
y
2
=
1
and a point
P
P
P
not on the curve. A line drawn from the point
P
P
P
intersects the curve at points
Q
Q
Q
and
R
R
R
. If the product
P
Q
⋅
P
R
PQ \cdot PR
P
Q
⋅
P
R
is independent of the slope of the line, then show that the curve is a circle.
Browse the problem library