Parametric Equations and Curves

This tutorial explores the rectangular hyperbola with parametric equations x = CT and y = C/T. It covers differentiating these equations to find the gradient, deriving the equation of the tangent and normal to the curve, and concludes with a reference to further examples on the website.

What is the parametric equation for the x-coordinate of a rectangular hyperbola?

• x = c/t

• x = t^2

• x = ct

• x = t/c

What is the parametric equation for the y-coordinate of a rectangular hyperbola?

• y = t^2

• y = t/c

• y = c/t

• y = ct

What is the first step in finding the gradient of a parametric curve?

• Differentiate y with respect to x

• Differentiate x with respect to t

• Use the chain rule

• Find dy/dx directly

What is the result of differentiating x = ct with respect to t?

• 1/c

• 0

• c

• t

What is the result of differentiating y = c/t with respect to t?

• -c/t^2

• c

• c/t^2

• t/c

How do you find dy/dx using the chain rule?

• Multiply dy/dt by dx/dt

• Divide dx/dt by dy/dt

• Divide dy/dt by dx/dt

• Multiply dx/dt by dy/dt

What is the general form of the equation of a tangent line?

• y = mx + c

• y - y1 = m(x - x1)

• y = x^2 + c

• y = c/x

What is the gradient of the tangent line at any point on the curve?

• -1/t^2

• 1/t^2

• -t^2

• t^2

What is the simplified form of the tangent equation after clearing fractions?

• x - y + ct = 0

• x + y - ct = 0

• x - t^2y + 2ct = 0

• x + t^2y - 2ct = 0

What is the negative reciprocal of the gradient of the tangent line?

• -t^2

• t^2

• 1/t^2

• -1/t^2