Exercises for Question Type 2: Tangents to implicitly defined curves

Question 1

Skill question

Use implicit differentiation to find the equation of the tangent line to the curve $x^{2} y - y^{2} = 0$ at the point $(1, 1)$ .

[6]

Question 2

Skill question

Find the equation of the tangent line to the curve $e^{x} + e^{y} = 2 e$ at the point $(1, 1)$ .

[6]

Question 3

Skill question

Find the equation of the tangent line to the curve $ln (x) + ln (y) = 0$ at the point $(1, 1)$ .

[5]

Question 4

Skill question

Find the equation of the tangent line to the curve $e^{x} + x y = e + 1$ at the point $(1, 1)$ .

[6]

Question 5

Skill question

Find the equation of the tangent line to the curve $x^{3} + y^{3} = 2$ at the point $(1, 1)$ .

[5]

Question 6

Skill question

Find the equation of the tangent line to the curve $ln (x y) = 0$ at the point $(1, 1)$ .

[6]

Question 7

Skill question

Find the equation of the tangent line to the curve $x y + y^{2} = 2$ at the point $(1, 1)$ .

[5]

Question 8

Skill question

Find the equation of the tangent line to the curve $x^{2} + y^{2} + x y = 3$ at the point $(1, 1)$ .

[6]

Question 9

Skill question

Find the equation of the tangent line to the curve $arctan (\frac{y}{x}) = \frac{π}{4}$ at the point $(1, 1)$ .

[4]

Question 10

Skill question

Find the equation of the tangent line to the curve $x^{2} + y^{2} = 2$ at the point $(1, 1)$ .

[6]

Question 11

Skill question

Find the equation of the tangent line to the curve $sin (x y) = sin (1)$ at the point $(1, 1)$ .

[6]

Question 12

Skill question

Find the equation of the tangent line to the curve $y^{2} = x + sin (x) - sin (1)$ at the point $(1, 1)$ .

[6]

IB Mathematics Analysis and Approaches Question Type 2: Tangents to Implicitly Defined Curves Exercises