Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
A normal inclined at an angle of
45
∘
45^\circ
4
5
∘
to
x
x
x
-axis of the ellipse
x
2
a
2
+
y
2
b
2
=
1
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
a
2
x
2
+
b
2
y
2
=
1
is drawn. It meets the major and minor axes in
P
P
P
and
Q
Q
Q
respectively. If
C
C
C
is the centre of the ellipse, prove that area of
Δ
C
P
Q
\Delta CPQ
Δ
C
P
Q
is
(
a
2
−
b
2
)
2
2
(
a
2
+
b
2
)
\frac{(a^2 - b^2)^2}{2(a^2 + b^2)}
2
(
a
2
+
b
2
)
(
a
2
−
b
2
)
2
sq units.
Browse the problem library