# Worksheet: Finding the Tangent Equation and the Normal Equation of a Parametrically Defined Curve

Q1:

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

• A
• B
• C
• D
• E

Q2:

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

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• B
• C
• D
• E

Q3:

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

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• B
• C
• D
• E

Q4:

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

• A
• B
• C
• D
• E

Q5:

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

• A
• B
• C
• D

Q6:

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

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• B
• C
• D
• E

Q7:

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

• A
• B
• C
• D
• E

Q8:

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

• A
• B
• C
• D
• E

Q9:

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

• A
• B
• C
• D
• E

Q10:

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

• A
• B
• C
• D

Q11:

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

• A
• B
• C
• D

Q12:

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

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• B
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• D

Q13:

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

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• D

Q14:

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

• A
• B
• C
• D

Q15:

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

Q16:

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.

Q17:

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.

Q18:

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 ,