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Worksheet: Finding the Tangent to 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.

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

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

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

Q17:

Consider the curve , .

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

  • Ano horizontal tangents.
  • B, , ,
  • C,
  • D
  • E,

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

  • Ano vertical tangents.
  • B
  • C,
  • D, , ,
  • E,

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 where is an integer
  • D, where is an integer
  • E