14 The curve \(C\) has polar equation
$$r = \frac { 4 } { 5 + 3 \cos \theta } \quad ( - \pi < \theta \leq \pi )$$
14
- Show that \(r\) takes values in the range \(\frac { 1 } { k } \leq r \leq k\), where \(k\) is an integer.
[0pt]
[2 marks]
14 - Find the Cartesian equation of \(C\) in the form \(y ^ { 2 } = \mathrm { f } ( x )\)
14
- The ellipse \(E\) has equation
$$y ^ { 2 } + \frac { 16 x ^ { 2 } } { 25 } = 1$$
Find the transformation that maps the graph of \(E\) onto \(C\)
[0pt]
[4 marks]
| 15 | Find the general solution of the differential equation \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 3 \frac { \mathrm {~d} y } { \mathrm {~d} x } - 4 y = \cos 2 x + 5 x\) |