{"id":270257,"date":"2022-09-10T14:57:21","date_gmt":"2022-09-10T09:27:21","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-angle-between-pair-of-tangents-drawn-to-the-ellipse-3x22y25-from-the-point-1-2-is\/"},"modified":"2022-09-10T14:57:21","modified_gmt":"2022-09-10T09:27:21","slug":"the-angle-between-pair-of-tangents-drawn-to-the-ellipse-3x22y25-from-the-point-1-2-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-angle-between-pair-of-tangents-drawn-to-the-ellipse3x2\/","title":{"rendered":"The angle between pair of tangents drawn to the ellipse\u00a03×2+2y2=5\u00a0from the point (1, 2) is \u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The angle between pair of tangents drawn to the ellipse\u00a03x2+2y2=5\u00a0from the point (1, 2) is \u00a0","custom_permalink":"question\/mathematics\/the-angle-between-pair-of-tangents-drawn-to-the-ellipse3x2\/"},"categories":[],"acf":{"question":"

The angle between pair of tangents drawn to the ellipse 3<\/mn>x<\/mi>2<\/mn><\/msup>+<\/mo>2<\/mn>y<\/mi>2<\/mn><\/msup>=<\/mo>5<\/mn><\/math> from the point (1, 2) is  <\/p>","options":[{"option":"

tan<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>\u2061<\/mo>(<\/mo>12<\/mn>\/<\/mo>5<\/mn>)<\/mo><\/mtd><\/mtr> <\/mtd><\/mtr><\/mtable><\/math><\/p>","correct":false},{"option":"

tan<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>\u2061<\/mo>(<\/mo>6<\/mn>\/<\/mo>5<\/mn><\/msqrt>)<\/mo><\/mtd><\/mtr> <\/mtd><\/mtr><\/mtable><\/math><\/p>","correct":false},{"option":"

tan<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>\u2061<\/mo>(<\/mo>12<\/mn>\/<\/mo>5<\/mn><\/msqrt>)<\/mo><\/math><\/p>","correct":true},{"option":"

tan<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>\u2061<\/mo>(<\/mo>8<\/mn>\/<\/mo>5<\/mn><\/msqrt>)<\/mo><\/math><\/p>","correct":false}],"solution":"

S<\/mi>S<\/mi>11<\/mn><\/msub>=<\/mo>S<\/mi>1<\/mn><\/msub>2<\/mn><\/msup><\/math><\/p>

\u2234<\/mo> <\/mspace>\u2005\u2005\u2005\u2005<\/mo>3<\/mn>x<\/mi>2<\/mn><\/msup>+<\/mo>2<\/mn>y<\/mi>2<\/mn><\/msup>\u2212<\/mo>5<\/mn><\/mrow><\/mfenced>3<\/mn>(<\/mo>1<\/mn>2<\/mn><\/msup>)<\/mo>+<\/mo>2<\/mn>(<\/mo>2<\/mn>2<\/mn><\/msup>)<\/mo>\u2212<\/mo>5<\/mn><\/mrow><\/mfenced>=<\/mo>(<\/mo>3<\/mn>x<\/mi>.1<\/mn>+<\/mo>2<\/mn>y<\/mi>.2<\/mn>\u2212<\/mo>5<\/mn>)<\/mo>2<\/mn><\/msup><\/mrow><\/mtd><\/mtr>\u21d2<\/mo> <\/mspace>9<\/mn>x<\/mi>2<\/mn><\/msup>\u2212<\/mo>4<\/mn>y<\/mi>2<\/mn><\/msup>\u2212<\/mo>24<\/mn>x<\/mi>y<\/mi>+<\/mo>30<\/mn>x<\/mi>+<\/mo>40<\/mn>y<\/mi>\u2212<\/mo>55<\/mn>=<\/mo>0<\/mn><\/mtd><\/mtr>\u2005\u2005\u2005\u2005<\/mo>tan<\/mi>\u2061<\/mo>\u03b8<\/mi>=<\/mo>2<\/mn>\u22c5<\/mo>h<\/mi>2<\/mn><\/msup>\u2212<\/mo>a<\/mi>b<\/mi><\/mrow><\/mfenced><\/msqrt>a<\/mi>+<\/mo>b<\/mi><\/mrow><\/mfrac>,<\/mo> <\/mspace>a<\/mi>=<\/mo>9<\/mn>,<\/mo>b<\/mi>=<\/mo>\u2212<\/mo>4<\/mn>,<\/mo>h<\/mi>=<\/mo>\u2212<\/mo>12<\/mn><\/mtd><\/mtr><\/mtable><\/math><\/p>

Alt. The ellipse is of the form x<\/mi>2<\/mn><\/msup>b<\/mi>2<\/mn><\/msup><\/mfrac>+<\/mo>y<\/mi>2<\/mn><\/msup>a<\/mi>2<\/mn><\/msup><\/mfrac>=<\/mo>1<\/mn>a<\/mi>2<\/mn><\/msup>><\/mo>b<\/mi>2<\/mn><\/msup><\/mrow><\/mfenced><\/math> the equation of any tangent to it is <\/p>

x<\/mi>=<\/mo>m<\/mi>y<\/mi>+<\/mo>a<\/mi>2<\/mn><\/msup>m<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>2<\/mn><\/msup><\/msqrt><\/math> It passes through ( 1, 2l  <\/p>

\u2234<\/mo> <\/mspace>(<\/mo>1<\/mn>\u2212<\/mo>2<\/mn>m<\/mi>)<\/mo>2<\/mn><\/msup>=<\/mo>5<\/mn>6<\/mn><\/mfrac>3<\/mn>m<\/mi>2<\/mn><\/msup>+<\/mo>2<\/mn><\/mrow><\/mfenced><\/math><\/p>

\u21d2<\/mo><\/math> 9<\/mn>m<\/mi>2<\/mn><\/msup>\u2212<\/mo>24<\/mn>m<\/mi>\u2212<\/mo>4<\/mn>=<\/mo>0<\/mn><\/math> <\/p>

tan<\/mi>\u2061<\/mo>\u03b8<\/mi>=<\/mo>m<\/mi>1<\/mn><\/msub>\u2212<\/mo>m<\/mi>2<\/mn><\/msub><\/mrow>1<\/mn>+<\/mo>m<\/mi>1<\/mn><\/msub>m<\/mi>2<\/mn><\/msub><\/mrow><\/mfrac>=<\/mo>m<\/mi>1<\/mn><\/msub>+<\/mo>m<\/mi>2<\/mn><\/msub><\/mrow><\/mfenced>2<\/mn><\/msup>\u2212<\/mo>4<\/mn>m<\/mi>1<\/mn><\/msub>m<\/mi>2<\/mn><\/msub><\/mrow>1<\/mn>+<\/mo>m<\/mi>1<\/mn><\/msub>m<\/mi>2<\/mn><\/msub><\/mrow><\/mfrac><\/mtd><\/mtr>=<\/mo>720<\/mn><\/msqrt>5<\/mn><\/mfrac>=<\/mo>12<\/mn>5<\/mn><\/msqrt><\/mrow>5<\/mn><\/mfrac>=<\/mo>12<\/mn>5<\/mn><\/msqrt><\/mfrac> etc. <\/mtext><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"\nThe angle between pair of tangents drawn to the ellipse\u00a03x2+2y2=5\u00a0from the point (1, 2) is \u00a0 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The angle between pair of tangents drawn to the ellipse\u00a03x2+2y2=5\u00a0from the point (1, 2) is \u00a0\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-angle-between-pair-of-tangents-drawn-to-the-ellipse3x2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The angle between pair of tangents drawn to the ellipse\u00a03x2+2y2=5\u00a0from the point (1, 2) is \u00a0 - 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