Examples and practice
Parametric equations
Back to lessonPractice section 1 · Questions 1–6
Find axial intercepts using the appropriate coordinate · Sketch two parameterised curves with their full allowed ranges · +4 more
- Find axial intercepts using the appropriate coordinate
- Sketch two parameterised curves with their full allowed ranges
- Sketch a scaled rational curve and verify its asymptote
- Retain the positive branch when eliminating a radical parameter
- Eliminate trigonometric parameters to identify an ellipse
- Eliminate reciprocal parameters and retain both hyperbola branches
Practice section 2 · Questions 7–12
Synchronise projectile flight with an approaching target · Divide parameter derivatives to obtain the Cartesian gradient · +4 more
- Synchronise projectile flight with an approaching target
- Divide parameter derivatives to obtain the Cartesian gradient
- Practise reciprocal and trigonometric derivative ratios
- Find tangent and normal equations with a scale parameter
- Trace a moving midpoint locus from tangent intercepts
- Find a normal and distinguish its second curve intersection
Practice section 3 · Questions 13–18
Find all axial intersections of a parametric curve · Eliminate a reciprocal parameter and sketch the hyperbola · +4 more
- Find all axial intersections of a parametric curve
- Eliminate a reciprocal parameter and sketch the hyperbola
- Eliminate exponential and trigonometric parameters
- Find a tangent, normal and exact triangle area
- Differentiate a restricted parametric curve and find an intersection
- Find the locus of a tangent-segment midpoint
Practice section 4 · Questions 19–24
Test whether a tangent meets the curve again · Sketch a cycloid and locate a normal intercept · +4 more
- Test whether a tangent meets the curve again
- Sketch a cycloid and locate a normal intercept
- Eliminate t using a cancelling linear combination
- Eliminate a positive parameter and retain closed endpoints
- Keep the trigonometric range and solve an intersection exactly
- Differentiate a rational and logarithmic parametrisation
Practice section 5 · Questions 25–30
Solve the exact parameter values for a prescribed gradient · Separate a vertical tangent from an excluded endpoint · +4 more
- Solve the exact parameter values for a prescribed gradient
- Separate a vertical tangent from an excluded endpoint
- Derive an ellipse tangent without losing its vertical cases
- Use a horizontal normal to identify a vertical tangent
- Obtain a tangent-intercept triangle and qualify its endpoint
- Remove the original intersection before using a discriminant
Practice section 6 · Question 31
Recover a hyperbola from tangent-intercept midpoints