# Worksheet: Implicit Differentiation

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

**Q7: **

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

- A
- B
- C
- D

**Q8: **

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

- A
- B
- C,
- D,

**Q9: **

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

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

**Q10: **

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

- A
- B
- C
- D

**Q11: **

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

**Q12: **

Given that , determine by implicit differentiation.

- A
- B
- C
- D
- E

**Q13: **

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,

**Q14: **

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

- A
- B
- C
- D

**Q15: **

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

**Q16: **

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

- A
- B
- C
- D

**Q17: **

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

- A
- B
- C
- D

**Q18: **

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

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

**Q19: **

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

- A
- B
- C
- D

**Q20: **

Given that , find .

- A
- B
- C16
- D

**Q21: **

If , find the value of at .

**Q22: **

Find, for , the tangent to that has slope , giving your equation in terms of .

- A
- B
- C
- D

**Q23: **

Find the equation of the tangent to that passes through .

- A
- B
- C
- D

**Q24: **

A tangent to has slope . What is the equation of this line?

- A
- B
- C
- D

**Q25: **

Find , given that .

- A
- B
- C
- D