Give the equation of the ellipse having foci at (-1, -1) and (-1, 7) and the length of the semi - minor axis is 8 units.
Hello fishlord40The centre of the ellipse is at the mid-point of the line joining the foci. So that's at . This means the equation will be of the form:The axis is along the line , so the major axis is vertical, having foci where , being the length of the semi-major axis and the eccentricity. This gives:The length of the semi-minor axis is the value of . So .
Finally, with an ellipse with a vertical major axis, we have:Eliminate to find , and hence the equation of the ellipse.
Grandad