# Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.7 | Set 1

Last Updated : 20 May, 2021

### Question 1. Find , when: x = at2 and y = 2at

Solution:

Given that x = at2, y = 2at

So,

Therefore,

### Question 2. Find , when: x = a(Î¸ + sinÎ¸) and y = a(1 – cosÎ¸)

Solution:

Here,

x = a(Î¸ + sinÎ¸)

Differentiating it with respect to Î¸,

and,

y = a(1 – cosÎ¸)

Differentiate it with respect to Î¸,

Using equation (1) and (2),

### Question 3. Find , when: x = acosÎ¸ and y = bsinÎ¸

Solution:

Then x = acosÎ¸ and y = bsinÎ¸

Then,

Therefore,

### Question 4. Find , when: x = aeÎ˜ (sinÎ¸ -cosÎ¸), y = aeÎ˜ (sinÎ¸ +cosÎ¸)

Solution:

Here,

x = aeÎ˜ (sinÎ¸ – cosÎ¸)

Differentiating it with respect to Î¸,

And,

y = aeÎ˜(sinÎ¸+cosÎ¸)

Differentiating it with respect to Î¸

Dividing equation (2) by equation (1)

### Question 5. Find , when: x = bsin2Î¸ and y = acos2Î¸

Solution:

Here,

x = bsin2Î¸ and y = acos2Î¸

Then,

### Question 6. Find , when: x = a(1 – cosÎ¸) and y = a(Î¸ +sinÎ¸) at Î¸ =

Solution:

Here,

x = a(1 – cosÎ¸) and y = a(Î¸ + sinÎ¸)

Then,

Therefore,

### Question 7. Find , when: and

Solution:

Here,

Differentiate it with respect to t,

and,

Differentiating it with respect to t,

Dividing equation (2) and (1)

### Question 8. Find , when: and

Solution:

Here,

Differentiating it with respect to t using quotient rule,

and,

Differentiating it with respect to t using quotient rule,

Dividing equation (2) by (1)

### Question 9. If x and y are connected parametrically by the equation, without eliminating the parameter, find when: x = a(cosÎ¸ +Î¸sinÎ¸), y = a(sinÎ¸ -Î¸cosÎ¸)

Solution:

The given equations are

x = a(cosÎ¸ +Î¸ sinÎ¸) and y = a(sinÎ¸ -Î¸cosÎ¸)

Then,

= a[-sinÎ¸ + Î¸cosÎ¸ + sinÎ¸] = aÎ¸cosÎ¸

= a[cosÎ¸ +Î¸sinÎ¸ -cosÎ¸]

= aÎ¸sinÎ¸

Therefore,

### Question 10. Find , when: and

Solution:

Here,

Differentiating it with respect to Î¸ using product rule,

and,

Differentiating it with respect to Î¸ using product rule and chain rule

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