# Worksheet: Tangents and Normal Equations of Parametric Curves

Q1:

Find an equation of the tangent to the curve , at the point corresponding to the value .

• A
• B
• C
• D
• E

Q2:

Find an equation of the tangent to the curve , at the point corresponding to the value .

• A
• B
• C
• D
• E

Q3:

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

• A
• B
• C
• D

Q4:

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

• A
• B
• C
• D
• E

Q5:

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

• A , ,
• B ,
• C ,
• D
• EThere are no horizontal tangents.

Find all points on this curve where the tangent is vertical.

• A ,
• B ,
• C , ,
• D
• EThere are no vertical tangents.

Q6:

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

• A
• B
• C
• D
• E

Q7:

A cycloid curve is given by the equations and .

Find the tangent to the cycloid at the point where .

• A
• B
• C
• D
• E

Find all points on the curve where the tangent is horizontal.

• A where is an integer
• B where is an integer
• C , where is an integer
• D where is an integer
• E , where is an integer

Find all points on the curve where the tangent is vertical.

• A , where is an integer
• B where is an integer
• C where is an integer
• D , where is an integer
• E where is an integer

Q8:

Find the value of at which the curve , has a vertical tangent.

• A ,
• B
• C
• D ,
• E

Q9:

Find all possible equations of the tangents to the curve , that pass through the point .

• A ,
• B
• C
• D ,
• E , ,

Q10:

Find the equation of the tangent to the curve , at the point corresponding to the value .

• A
• B
• C
• D
• E

Q11:

A curve is defined by the parametric equations and .

Find the two equations of the tangents to curve on the point at .

• A ,
• B ,
• C ,
• D ,
• E ,

Find all possible points on where the tangent is horizontal.

• A ,
• B
• C , ,
• D
• E ,

Find all possible points on where the tangent is vertical.

• A ,
• B ,
• C
• D , ,
• E

Q12:

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

• A
• B
• C
• D

Q13:

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

• A
• B
• C
• D
• E

Q14:

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

• A
• B ,
• C , , ,
• D ,
• Eno horizontal tangents.

Find all points on this curve where the tangent is vertical.

• A ,
• B
• C , , ,
• D ,
• Eno vertical tangents.

Q15:

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

• A , , ,
• B ,
• C
• D ,
• EThere are no horizontal tangents.

Find all points on this curve where the tangent is vertical.

• A ,
• B
• C , , ,
• D ,
• EThere are no vertical tangents.

Q16:

Determine the equation of the normal to the curve , at .

• A
• B
• C
• D

Q17:

Consider the curve , .

Find all points on this curve where the tangent is horizontal.

• A
• B
• C ,
• D ,
• EThere are no horizontal tangents.

Find all points on this curve where the tangent is vertical.

• AThere are no vertical tangents.
• B
• C
• D ,
• E ,

Q18:

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

• A
• B
• C
• D

Q19:

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

• A
• B
• C
• D

Q20:

Find an equation of the tangent to the curve , at the point corresponding to the value .

• A
• B
• C
• D
• E

Q21:

Find the equation of the normal to the curves and at .

• A
• B
• C
• D

Q22:

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

• A
• B
• C
• D

Q23:

Find the slope of the tangent to the astroid , in terms of .

• A
• B
• C
• D
• E

Q24:

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

• A
• B
• C
• D
• E

Q25:

Given that , and , determine the equation of the tangent to the curve at .

• A
• B
• C
• D