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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 .

  • A
  • B
  • C
  • D
  • E

Q3:

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

  • A
  • 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 .

  • A
  • 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 .

  • A
  • B
  • C
  • D

Q13:

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

  • A
  • B
  • C
  • 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 ,