# Class 12 Maths NCERT Solutions for Chapter 5 Continuity and Differentiability Exercise 5.6

### Continuity and Differentiability Exercise 5.6 Solutions

1. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx .
x = 2at2 , y = at4

Solution

The given equations are x = 2at2 , y = at4

2. If x and y are connected parametrically by the equations x = a cos Î¸, y = b cos Î¸, without eliminating the parameter, find dy/dx .

Solution

The given equations are x = a cos Î¸, y = b cos Î¸

3. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx .
x = sin t, y = cos 2t

Solution

The given equations are x = sin t, y = cos 2t

Solution

4. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = 4t, y = 4/y
Solution
The given equations are x = 4t, y = 4/y

5. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = cos Î¸- cos 2Î¸, y = sin Î¸ - sin 2Î¸
Solution
The given equations are x = cos Î¸- cos 2Î¸, y = sin Î¸ - sin 2Î¸

6. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = a (Î¸ – sin Î¸), y = a (1 + cos Î¸)

Solution

The given equations are x =  a (Î¸ – sin Î¸), y = a (1 + cos Î¸)

7. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = sin3t/√(cos 2t) , y = cos3t/√(cos 2t)

Solution

The given equations are x = sin3t/√(cos 2t) and  y = cos3t/√(cos 2t)

8. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = a[cos t + log tan (t/2) ], y = a sin t

Solution

The given equation are x = a[cos t + log tan (t/2) ], y = a sin t

9. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = a sec Î¸, y = b tan Î¸

Solution

The given equations are x = a sec Î¸, y = b tan Î¸

10. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = a (cos Î¸ + Î¸ sin Î¸), y = a (sin Î¸ – Î¸ cos Î¸)

Solution

The given equations are x = a (cos Î¸ + Î¸ sin Î¸), y = a (sin Î¸ – Î¸ cos Î¸)

11. If x = √(asin – 1), y = √(acos – 1) show that dy/dx = -y/x

Solution

The given equations are  x = √(asin – 1) and  y = √(acos – 1)

Hence, proved.