# Worksheet: Tangents and Normals to Graphs of Implicit Functions

Q1:

Determine the points on the curve at which the tangent is perpendicular to the line .

• A ,
• B ,
• C ,
• D ,
• E ,

Q2:

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

• A
• B
• C
• D

Q3:

Find the equation of the tangent to that has gradient .

• A
• B
• C
• D

Q4:

Do the curves and intersect orthogonally at the origin?

• Ayes
• Bno

Q5:

At a point on the curve with , , the tangent makes an angle of with the positive -axis. Find the equation of the tangent at that point.

• A
• B
• C
• D

Q6:

Find the points on the curve at which the tangent is parallel to the axis.

• A ,
• B
• C
• D ,

Q7:

Find the points that lie on the curve at which the tangent is parallel to line .

• A ,
• B ,
• C ,
• D ,

Q8:

A tangent to forms an isosceles triangle when taken with the positive - and -axes. What is the equation of this tangent?

• A
• B
• C
• D

Q9:

The point lies on the curve . Find and the equation of the tangent to the curve at this point.

• A , equation of the tangent:
• B , equation of the tangent:
• C , equation of the tangent:
• D , equation of the tangent:

Q10:

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

• A
• B
• C
• D
• E

Q11:

Determine the points on a curve at which the tangent to the curve is perpendicular to the straight line .

• A
• B
• C
• D

Q12:

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

• A
• B
• C
• D

Q13:

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

• A
• B
• C
• D

Q14:

Find the equations of the tangent lines of the curves and at the intersection points, and state whether the curves intersect orthogonally or not.

• A , , , , intersect orthogonally
• B , , , , do not intersect orthogonally
• C , , , , do not intersect orthogonally
• D , , , , intersect orthogonally

Q15:

The two curves and intersect orthogonally. Find all the possible values of .

• A
• B25
• C50
• D

Q16:

Determine the gradient of the tangent to at its intersection with the -axis.

• A ,
• B ,
• C ,
• D ,
• E ,

Q17:

At a point on the curve with , , the tangent makes an angle of with the positive -axis. Find the equation of the normal at that point.

• A
• B
• C
• D

Q18:

Find the area of the triangle bounded by the -axis, the tangent, and the normal to the curve at the point to the nearest thousandth.

Q19:

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

• A
• B
• C
• D

Q20:

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

• A
• B
• C
• D
• E

Q21:

The tangent at to the curve makes a positive angle with the positive -axis. Find this angle.

• A
• B
• C
• D
• E

Q22:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D

Q23:

At the point , determine the equation of the normal to the curve represented by the equation .

• A
• B
• C
• D

Q24:

Find the points of where the angle between the tangent and the positive -axis has cosine .

• A ,
• B ,
• C ,
• D ,

Q25:

Find the equation of the tangent to the curve at .

• A
• B
• C
• D