6 An ellipse \(E\) has equation
$$\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 4 } = 1$$
- Sketch the ellipse \(E\), showing the coordinates of the points of intersection of the ellipse with the coordinate axes.
- The ellipse \(E\) is stretched with scale factor 2 parallel to the \(y\)-axis.
Find and simplify the equation of the curve after the stretch.
- The original ellipse, \(E\), is translated by the vector \(\left[ \begin{array} { l } a
b \end{array} \right]\). The equation of the translated ellipse is
$$4 x ^ { 2 } + 3 y ^ { 2 } - 8 x + 6 y = 5$$
Find the values of \(a\) and \(b\).