In this worksheet, we will practice using implicit differentiation to differentiate functions defined implicitly.

**Q1: **

Find the equation of the tangent to that has slope .

- A
- B
- C
- D

**Q2: **

Find the equation of the tangent to the curve at the point .

- A
- B
- C
- D
- E

**Q3: **

Given that , find .

- A
- B2
- C
- D

**Q5: **

Do the curves and intersect orthogonally at the origin?

- Ayes
- Bno

**Q6: **

Determine the equation of the tangent to the curve at the point .

- A
- B
- C
- D

**Q7: **

Find the slope of the tangent to the curve at the point .

- A
- B
- C
- D

**Q8: **

At a point on the curve with , , the tangent makes an angle of with the positive -axis. Find the equation of the tangent at that point.

- A
- B
- C
- D

**Q9: **

Find the equation of the tangent to the curve at the point .

- A
- B
- C
- D

**Q11: **

Find the points on the curve at which the tangent is parallel to the axis.

- A ,
- B
- C
- D ,

**Q12: **

Find the points that lie on the curve at which the tangent is parallel to line .

- A ,
- B ,
- C ,
- D ,

**Q13: **

Find the equation of the tangent to the curve at the point .

- A
- B
- C
- D

**Q14: **

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle to the nearest minute.

- A
- B
- C
- D

**Q15: **

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

**Q16: **

A tangent to forms an isosceles triangle when taken with the positive - and -axes. What is the equation of this tangent?

- A
- B
- C
- D

**Q17: **

Given that , determine by implicit differentiation.

- A
- B
- C
- D
- E

**Q18: **

Find the equations of the two tangents to the circle that are inclined to the positive -axis by an angle whose tangent is 2.

- A ,
- B ,
- C ,
- D ,

**Q19: **

Find the equation of the tangent to the curve at the point .

- A
- B
- C
- D

**Q20: **

The point lies on the curve . Find and the equation of the tangent to the curve at this point.

- A , equation of the tangent:
- B , equation of the tangent:
- C , equation of the tangent:
- D , equation of the tangent:

**Q21: **

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

- A
- B
- C
- D
- E

**Q22: **

Find the equation of the tangent to the curve at the point .

- A
- B
- C
- D

**Q23: **

Determine the points on a curve at which the tangent to the curve is perpendicular to the straight line .

- A
- B
- C
- D

**Q24: **

Find the equation of the normal to the curve at the point .

- A
- B
- C
- D

**Q25: **

Find the equations of the normals to the curve at the points on the -axis.

- A ,
- B ,
- C ,
- D ,