Find tangent equation at point

A question is this type if and only if it asks to find the equation of the tangent line to an implicitly defined curve at a specific point.

33 questions · Standard +0.2

1.07s Parametric and implicit differentiation
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OCR C4 Q3
7 marks Standard +0.3
3. A curve has the equation $$2 \sin 2 x - \tan y = 0$$
  1. Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in its simplest form in terms of \(x\) and \(y\).
  2. Show that the tangent to the curve at the point \(\left( \frac { \pi } { 6 } , \frac { \pi } { 3 } \right)\) has the equation $$y = \frac { 1 } { 2 } x + \frac { \pi } { 4 } .$$
OCR C4 2012 January Q3
8 marks Standard +0.3
3 The equation of a curve \(C\) is \(( x + 3 ) ( y + 4 ) = x ^ { 2 } + y ^ { 2 }\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
  2. The line \(2 y = x + 3\) meets \(C\) at two points. What can be said about the tangents to \(C\) at these points? Justify your answer.
  3. Find the equation of the tangent at the point ( 6,0 ), giving your answer in the form \(a x + b y = c\), where \(a , b\) and \(c\) are integers.
Edexcel C3 Q4
8 marks Standard +0.3
4. A curve has the equation \(x = y \sqrt { 1 - 2 y }\).
  1. Show that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { \sqrt { 1 - 2 y } } { 1 - 3 y } .$$ The point \(A\) on the curve has \(y\)-coordinate - 1 .
  2. Show that the equation of tangent to the curve at \(A\) can be written in the form $$\sqrt { 3 } x + p y + q = 0$$ where \(p\) and \(q\) are integers to be found.
Edexcel C4 Q2
8 marks Moderate -0.3
  1. A curve has the equation
$$4 \cos x + 2 \sin y = 3$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 \sin x \sec y\).
  2. Find an equation for the tangent to the curve at the point \(\left( \frac { \pi } { 3 } , \frac { \pi } { 6 } \right)\), giving your answer in the form \(a x + b y = c\), where \(a\) and \(b\) are integers.
Edexcel C4 2014 June Q1
7 marks Standard +0.3
A curve \(C\) has the equation $$x^3 + 2xy - x - y^3 - 20 = 0$$
  1. [(a)] Find \(\frac{dy}{dx}\) in terms of \(x\) and \(y\). \hfill [5]
  2. [(b)] Find an equation of the tangent to \(C\) at the point \((3, -2)\), giving your answer in the form \(ax + by + c = 0\), where \(a\), \(b\) and \(c\) are integers. \hfill [2]
OCR C3 2009 June Q6
7 marks Standard +0.3
\includegraphics{figure_3} The diagram shows the curve with equation \(x = (37 + 10y - 2y^2)^{\frac{1}{2}}\).
  1. Find an expression for \(\frac{dx}{dy}\) in terms of \(y\). [2]
  2. Hence find the equation of the tangent to the curve at the point \((7, 3)\), giving your answer in the form \(y = mx + c\). [5]
Edexcel C4 Q5
8 marks Standard +0.3
A curve has the equation $$x^2 - 3xy - y^2 = 12.$$
  1. Find an expression for \(\frac{dy}{dx}\) in terms of \(x\) and \(y\). [5]
  2. Find an equation for the tangent to the curve at the point \((2, -2)\). [3]
Edexcel C4 Q3
8 marks Standard +0.3
A curve has the equation $$2 \sin 2x - \tan y = 0.$$
  1. Find an expression for \(\frac{dy}{dx}\) in its simplest form in terms of \(x\) and \(y\). [5]
  2. Show that the tangent to the curve at the point \(\left(\frac{\pi}{6}, \frac{\pi}{3}\right)\) has the equation $$y = \frac{1}{2}x + \frac{\pi}{4}.$$ [3]