Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Prove that the chord of contact of tangents drawn from the point
(
h
,
k
)
(h, k)
(
h
,
k
)
to 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
will subtend a right angle at the centre, if
h
2
a
4
+
k
2
b
4
=
1
a
2
+
1
b
2
\frac{h^2}{a^4} + \frac{k^2}{b^4} = \frac{1}{a^2} + \frac{1}{b^2}
a
4
h
2
+
b
4
k
2
=
a
2
1
+
b
2
1
. Also, find the locus of
(
h
,
k
)
(h, k)
(
h
,
k
)
.
Browse the problem library