Question 935298
If you're asking about finding the length of the latus rectum of an ellipse, it is:
{{{2*b^2/a}}}<br>
If you're asking about how to find the endpoints of the latus rectum, then<ol><li>Determine if the ellipse is vertical or horizontal.</li><li>Find the center, ({{{h}}}, {{{k}}}), of the ellipse.</li><li>Find the "{{{c}}}" for the ellipse. "{{{c}}}" is the distance from the center of the ellipse to each focus. "{{{c}}}" is often found using the "{{{a}}}" and "{{{b}}}" from the equation of the ellipse and the equation {{{a^2 = b^2 + c^2}}}</li><li>Find half of the length of the latus rectum. IOW: {{{b^2/a}}}. We're going to call this number "{{{q}}}" in the next part.</li><li>The endpoints of the two latus rectum...<ul><li>for a horizontal ellipse: ({{{h+c}}}, {{{k+q}}}), ({{{h+c}}}, {{{k-q}}}), ({{{h-c}}}, {{{k+q}}}) and ({{{h-c}}}, {{{k-q}}})</li><li>for a vertical ellipse: ({{{h+q}}}, {{{k+c}}}), ({{{h+q}}}, {{{k-c}}}), ({{{h-q}}}, {{{k+c}}}) and ({{{h-q}}}, {{{k-c)}}}</li></ul></li></ol>