{"id":268542,"date":"2022-09-10T14:36:43","date_gmt":"2022-09-10T09:06:43","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-straight-line-passing-through-the-point-84-and-cuts-y-axis-at-b-and-x-axis-at-a-the-locus-of-mid-point-of-ab-is\/"},"modified":"2022-09-10T14:36:43","modified_gmt":"2022-09-10T09:06:43","slug":"the-straight-line-passing-through-the-point-84-and-cuts-y-axis-at-b-and-x-axis-at-a-the-locus-of-mid-point-of-ab-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-straight-line-passing-through-the-point-84-and-cuts-y\/","title":{"rendered":"The straight line passing through the point (8,4) and cuts y-axis at B and x-axis at A. The locus of mid point of AB is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The straight line passing through the point (8,4) and cuts y-axis at B and x-axis at A. The locus of mid point of AB is","custom_permalink":"question\/mathematics\/the-straight-line-passing-through-the-point-84-and-cuts-y\/"},"categories":[],"acf":{"question":"<p>The straight line passing through the point (8,4) and cuts y-axis at B and x-axis at A. The locus of mid point of AB is<\/p>","options":[{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>xy<\/mi><mo>+<\/mo><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><mo>+<\/mo><mn>4<\/mn><mi mathvariant=\"normal\">y<\/mi><mo>=<\/mo><mn>64<\/mn><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>xy<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><mo>\u2212<\/mo><mn>4<\/mn><mi mathvariant=\"normal\">y<\/mi><mo>=<\/mo><mn>0<\/mn><\/math><\/p>","correct":true},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>xy<\/mi><mo>\u2212<\/mo><mn>4<\/mn><mi mathvariant=\"normal\">x<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mi mathvariant=\"normal\">y<\/mi><mo>+<\/mo><mn>8<\/mn><mo>=<\/mo><mn>0<\/mn><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>xy<\/mi><mo>+<\/mo><mn>4<\/mn><mi mathvariant=\"normal\">x<\/mi><mo>+<\/mo><mn>2<\/mn><mi mathvariant=\"normal\">y<\/mi><mo>=<\/mo><mn>72<\/mn><\/math><\/p>","correct":false}],"solution":"<p>Let the eq of&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>AB<\/mi><mo>&nbsp;<\/mo><mi>i<\/mi><mi>s<\/mi><mo>&nbsp;<\/mo><mfrac><mi mathvariant=\"normal\">x<\/mi><mi mathvariant=\"normal\">a<\/mi><\/mfrac><mo>+<\/mo><mfrac><mi mathvariant=\"normal\">y<\/mi><mi mathvariant=\"normal\">b<\/mi><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/math>&nbsp;\u2026\u2026(1)<\/p><p>Let p(h,k) locus of mid point of AB.<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mi mathvariant=\"normal\">x<\/mi><mrow><mn>2<\/mn><mi mathvariant=\"normal\">h<\/mi><\/mrow><\/mfrac><mo>+<\/mo><mfrac><mi mathvariant=\"normal\">y<\/mi><mrow><mn>2<\/mn><mi mathvariant=\"normal\">k<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mn>1<\/mn><\/math>&nbsp;through the point &nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>(<\/mo><mi mathvariant=\"normal\">x<\/mi><mo>,<\/mo><mi mathvariant=\"normal\">y<\/mi><mo>)<\/mo><mo>=<\/mo><mo>(<\/mo><mn>8<\/mn><mo>,<\/mo><mn>4<\/mn><mo>)<\/mo><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">\u21d2<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>(<\/mo><mn>8<\/mn><mi mathvariant=\"normal\">k<\/mi><mo>+<\/mo><mn>4<\/mn><mi mathvariant=\"normal\">h<\/mi><mo>)<\/mo><mo>=<\/mo><mi>hk<\/mi><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math>The locus of p is&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>xy<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mi mathvariant=\"normal\">x<\/mi><mo>\u2212<\/mo><mn>4<\/mn><mi mathvariant=\"normal\">y<\/mi><mo>=<\/mo><mn>0<\/mn><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The straight line passing through the point (8,4) and cuts y-axis at B and x-axis at A. 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