form a partial differential equation by eliminating arbitrary constants from z=(√x+ a)(√y+b)
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Answer:
Given: Equation of ellipse⇒
a
2
x
2
+
b
2
y
2
=1
Concept:
Here we see that there are two arbitrary constants(a and b) in equation of ellipse thus we have to get a differential equation of 2nd order for eliminating all constants.
Solution:
Differentiating given equation with respect to x, we get:
a
2
2x
+
b
2
2y
(
dx
dy
)=0
⇒
x
y
(
dx
dy
)=
a
2
−b
2
Again differentating with respect to x, we get:
⇒
x
y
(
dx
2
d
2
y
)+
x
2
x
dx
dy
−y
dx
dy
=0
⇒xy
dx
2
d
2
y
+x(
dx
dy
)
2
−y
dx
dy
=0
which is the required differential equation
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