Find tangent equation at parameter

A question is this type if and only if it asks to find the equation of the tangent line to a parametric curve at a specific parameter value or point.

29 questions · Standard +0.1

1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation
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Pre-U Pre-U 9794/2 2016 Specimen Q8
8 marks Moderate -0.3
8 The parametric equations of a curve are $$x = \mathrm { e } ^ { 2 t } - 5 t , \quad y = \mathrm { e } ^ { 2 t } - 3 t .$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
  2. Find the equation of the tangent to the curve at the point when \(t = 0\), giving your answer in the form \(a y + b x + c = 0\) where \(a , b\) and \(c\) are integers.
Pre-U Pre-U 9794/2 2019 Specimen Q8
5 marks Moderate -0.3
8 The parametric equations of a curve are $$x = \mathrm { e } ^ { 2 t } - 5 t , \quad y = \mathrm { e } ^ { 2 t } - 3 t .$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
  2. Find the equation of the tangent to the curve at the point when \(t = 0\), giving your answer in the form \(a y + b x + c = 0\) where \(a , b\) and \(c\) are integers.
Edexcel C4 Q6
12 marks Standard +0.3
A curve has parametric equations $$x = 2\cot t, \quad y = 2\sin^2 t, \quad 0 < t \leq \frac{\pi}{2}.$$
  1. Find an expression for \(\frac{dy}{dx}\) in terms of the parameter \(t\). [4]
  2. Find an equation of the tangent to the curve at the point where \(t = \frac{\pi}{4}\). [4]
  3. Find a cartesian equation of the curve in the form \(y = f(x)\). State the domain on which the curve is defined. [4]
WJEC Unit 3 2024 June Q11
10 marks Standard +0.3
A curve is defined parametrically by $$x = 2\theta + \sin 2\theta, \quad y = 1 + \cos 2\theta.$$
  1. Show that the gradient of the curve at the point with parameter \(\theta\) is \(-\tan\theta\). [6]
  2. Find the equation of the tangent to the curve at the point where \(\theta = \frac{\pi}{4}\). [4]