.If 2+ 2/ + = +/ 2+2 prove that / = /d
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Answer:
2(x−a)+2(y−b)
dx
dy
=0
⇒
dx
dy
=
y−b
−(x−a)
dx
2
d
2
y
=
(y−b)
2
(1−0)(y−b)−(
dx
dy
−0)(x−a)
=
(y−b)
2
(y−b)−(x−a)
dx
dy
=
(y−b)
2
(y−b)−(x−a)(
y−b
−(x−a)
)
⇒
dx
2
d
2
y
=
(y−b)
3
(y−b)
2
+(x−a)
2
dx
2
d
2
y
[1+(
dx
dy
)
2
]
2
3
=
(y−b)
3
(y−b)
2
+(x−a)
2
[1+(
y−b
−(x−a)
)
2
]
2
3
=
(y−b)
2
(y−b)
2
+(x−a)
2
×
(y−b)
1
[
(y−b)
2
(y−b)
2
+(x−a)
2
]
2
3
=
(y−b)
1
[
(y−b)
2
(y−b)
2
+(x−a)
2
]
2
2
=[
(y−b)
2
(y−b)
2
+(x−a)
2
]×
1
y−b
=[
(y−b)
(y−b)
2
+(x−a)
2
]
=(y−b)+
y−b
(x−a)
2
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