Question

If a is a parameter, then the equation f(x, y, a) = 0 represents
A. one-parameter family of curves
C. three-parameters family of curves
B. two-parameters family of curves
D. all of the above
ОА
OB
Ос
♡
OD​

Answer 1

Answer

Given family of curves

y

2

=2c(x+

c

) ...(i)

On differentiating both sides, we get

2y

dx

dy

=2c(1+0)⇒c=y

dx

dy

From equation (i), we have

y

2

=2y

dx

dy

{x+(y

dx

dy

)

1/2

}

⇒(y

2

−2xy

dx

dy

)=2(y

dx

dy

)

3/2

On squaring both sides, we get

(y

2

−2xy

dx

dy

)

2

=4(y

dx

dy

)

3

So,

Order=1 (Order of a differential equation is the order of the highest derivative (also known as differential coefficient) present in the equation.)

Degree=3 (The degree of differential equation is represented by the power of the highest order derivative in the given differential equation.)

Answer 2

Answer:

Option A

There is only one parameter in the family of curves.

Step-by-step explanation:

• If $f(x,y,a) = 0$ is a function where $a$ gives rise to the different members of the family.
• The value of $a$ is different for different curves of the family and is same for the same members of the family.
• The equation $f(x,y,a) = 0$  represents family of curves for different value of $a$, also called parameter of the family.

Hence, there is only one parameter in the family of curves.

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