Course Content

0/1

0/3

0/5

0/3

0/2

0/4

0/2

0/1

0/5

5.3 Ellipse 椭圆

1. Find the centre, vertex, axis of symmetry, major semi-axis, minor semi-axis, eccentricity, focus, directrix and length of latus rectum for the following ellipse and sketch the graph.

(a) (b) (c) (d) (e)      2. Find the equation of the ellipse with center at (-3, 1), one of vertices at (-5, 1), length of latus rectum equal to 1 and

(a) major axis parallel x-axis,

(b) major axis parallel y-axis,

(a) (b) 3. Find the equation of the ellipse which has same eccentricity and left directrix with ellipse , and also take its right focus to be the left focus. 4. Given that the major axis of an ellipse is 4, y-axis be its directrix, the left focus is on the parabola . Find the equation of the ellipse when eccentricity is . 5. Given that F (2, -2), F (2, 0) are the foci of a ellipse, straight line y = 3 is a directrix of the ellipse, find the equation of the ellipse. 6. Find the equation of the ellipse with vertices at (0, -1) and (12, -1), a focus at .  