st","extracted_subject":"MATH","extracted_chapter":"CONIC SECTIONS","extracted_topic":"ELLIPSE","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1844.png?top_left_x=1064&top_left_y=1228&width=532&height=340&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31df6a","slug":"the-length-of-the-latus-rectum-of-an-ellipse-is-fr","content":"The length of the latus rectum of an ellipse is \$\\frac{1}{3}\$of the major axis. Its eccentricity is","options":[{"_id":"68a931407f15af4716d2df7e","text":"\$\\frac{2}{3}\$","sequence":0,"isCorrect":false},{"_id":"68a931407f15af4716d2df7f","text":"\$\\sqrt{\\frac{2}{3}}\$","sequence":1,"isCorrect":true},{"_id":"68a931407f15af4716d2df80","text":"\$\\frac{5 \\times 4 \\times 3}{7^{3}}\$","sequence":2,"isCorrect":false},{"_id":"68a931407f15af4716d2df81","text":"\$\\left( \\frac{3}{4} \\right)^{4}\$","sequence":3,"isCorrect":false}],"correct_answer":"$$\\sqrt{\\frac{2}{3}}$","explanation":"\$\\frac{2b^{2}}{a}\$= \$\\frac{1}{3}\$ (2a)\n\ñ 3b² = a² ̃ 3a² (1 – e²) = a²\n\ñ 1 – e² =\$\\frac{1}{3}\$̃ e² =\$\\frac{2}{3}\$̃ e = \$\\sqrt{\\frac{2}{3}}\$","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.272Z","__v":0,"vector_store_id":"a3f32538-1697-4b53-b140-3d0ed536e447","updated_at":"2024-08-30T21:49:37.272Z","isStarred":false},"params":{"questionSlug":"the-length-of-the-latus-rectum-of-an-ellipse-is-fr"}}]}]]

Question: The length of the latus rectum of an ellipse is \(\frac{1}{3}\)of the major axis. Its eccentricity i...

Solution