MathDB
Problems
Contests
National and Regional Contests
India Contests
ISI Entrance Examination
2020 ISI Entrance Examination
6
ISI 2020 : Problem 6
ISI 2020 : Problem 6
Source: B.Stat & B.Math Entrance Exam 2020
September 20, 2020
isi
2020
calculus
Problem Statement
Prove that the family of curves
x
2
a
2
+
λ
+
y
2
b
2
+
λ
=
1
\frac{x^2}{a^2+\lambda}+\frac{y^2}{b^2+\lambda}=1
a
2
+
λ
x
2
+
b
2
+
λ
y
2
=
1
satisfies
d
y
d
x
(
a
2
−
b
2
)
=
(
x
+
y
d
y
d
x
)
(
x
d
y
d
x
−
y
)
\frac{dy}{dx}(a^2-b^2)=\left(x+y\frac{dy}{dx}\right)\left(x\frac{dy}{dx}-y\right)
d
x
d
y
(
a
2
−
b
2
)
=
(
x
+
y
d
x
d
y
)
(
x
d
x
d
y
−
y
)
Back to Problems
View on AoPS