14 Curve \(C _ { 1 }\) has equation
$$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1$$
14
- Curve \(C _ { 2 }\) is a reflection of \(C _ { 1 }\) in the line \(y = x\)
Write down an equation of \(C _ { 2 }\)
14 - Curve \(C _ { 3 }\) is a circle of radius 4 , centred at the origin.
Describe a single transformation which maps \(C _ { 1 }\) onto \(C _ { 3 }\)
14 - Curve \(C _ { 4 }\) is a translation of \(C _ { 1 }\)
The positive \(x\)-axis and the positive \(y\)-axis are tangents to \(C _ { 4 }\)
14 - Sketch the graphs of \(C _ { 1 }\) and \(C _ { 4 }\) on the axes opposite. Indicate the coordinates of the \(x\) and \(y\) intercepts on your graphs.
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[2 marks]
14
- (ii) Determine the translation vector.
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[2 marks]
14 - (iii) The line \(y = m x + c\) is a tangent to both \(C _ { 1 }\) and \(C _ { 4 }\) Find the value of \(m\)