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Mathematics
Mathematics
Problem
A normal to the hyperbola
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
meets the axes in
M
M
M
and
N
N
N
and lines
M
P
MP
M
P
and
N
P
NP
N
P
are drawn perpendiculars to the axes meeting at
P
P
P
. Prove that the locus of
P
P
P
is the hyperbola
a
2
x
2
−
b
2
y
2
=
(
a
2
+
b
2
)
2
.
a^2 x^2 - b^2 y^2 = (a^2 + b^2)^2.
a
2
x
2
−
b
2
y
2
=
(
a
2
+
b
2
)
2
.
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