{"id":3343,"date":"2012-08-30T21:31:36","date_gmt":"2012-08-30T21:31:36","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=3343"},"modified":"2014-12-02T08:32:05","modified_gmt":"2014-12-02T08:32:05","slug":"geometry-locus-curves-and-sets","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/geometry-locus-curves-and-sets\/","title":{"rendered":"Geometry: Locus Curves and Sets"},"content":{"rendered":"

Usually a set of points which satisfy a particular geometric condition can be represented in the form of an algebraic equation. \u00a0For example, if we take a fixed distance r<\/em><\/strong> and a fixed point O<\/em><\/strong> then the set of all points which are at a constant distance r<\/em><\/strong> from the fixed point O<\/em><\/strong> forms a circle which can be expressed using an algebraic equation. Here the curve (circle) thus obtained is called the locus<\/em><\/strong> of the points which satisfy the above condition. Locus<\/em><\/strong> is mathematically defined as follows.<\/p>\n

\u201cLocus is a curve or the set of points which satisfy the given geometric condition\u201d.<\/em><\/strong><\/p>\n

Example:<\/strong><\/p>\n

If we take two points A<\/em><\/strong> and B<\/em><\/strong> then the set of all points which are equidistant from A<\/em><\/strong> and B<\/em><\/strong> is the perpendicular bisector of the line segment AB.<\/p>\n

Finding the equation of locus:<\/h5>\n

Step-1: <\/strong>Take any arbitrary point P(x,y) on the locus.<\/p>\n

Step-2: <\/strong>\u00a0Write the geometric condition to be satisfied by P according the problem.<\/p>\n

Step-3: <\/strong>Simplify the above equation according to the information provided to get the corresponding algebraic equation of the locus.<\/p>\n

Example-1:<\/strong><\/span><\/p>\n

Find the locus of a point which is at a distance of 5 units from A(4,-3).<\/p>\n

Solution:<\/strong><\/em><\/p>\n

Let P(x,y) be a point on the locus.<\/p>\n

The given geometric condition is,<\/p>\n

PA=5<\/p>\n

\u221a[(x-4)2<\/sup> +(y+3)2<\/sup>] = 5<\/p>\n

Squaring on both sides,<\/p>\n

(x-4)2<\/sup> +(y+3)2<\/sup>=25<\/p>\n

x2<\/sup> +16-8x+y2<\/sup>+9+6y=25<\/p>\n

x2<\/sup>+y2<\/sup>-8x+6y=0 is the equation of locus.<\/strong><\/p>\n

Example-2:<\/strong><\/strong><\/span><\/p>\n

Find the locus of a point which is equidistant from the points A(-3,2) and B(0,4).<\/p>\n

Solution:<\/strong><\/em><\/p>\n

Let P(x,y) be a point on the locus.<\/p>\n

The given geometric condition is,<\/p>\n

PA=PB<\/p>\n

\u221a[(x+3)2<\/sup> +(y-2)2<\/sup>] = \u221a[(x-0)2<\/sup> +(y-4)2<\/sup>]\n

Squaring on both sides,<\/p>\n

(x+3)2<\/sup> +(y-2)2<\/sup> = (x-0)2<\/sup> +(y-4)2<\/sup><\/p>\n

x2<\/sup> +9+6x+y2<\/sup>+4-4y= x2<\/sup> +y2<\/sup>+16-8y<\/p>\n

Simplifying the above equation,<\/p>\n

6x + 4y = 3, which is the required equation of locus.<\/p>\n

Still need help with Mathematics? Please read more about our Mathematics tutoring services<\/a>.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Pasadena visit: Tutoring in Pasadena . <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Usually a set of points which satisfy a particular geometric condition can be represented in the form of an algebraic equation. \u00a0For example, if we take a fixed distance r and a fixed point O then the set of all points which are at a constant distance r from the fixed point O forms a […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[73,368,443,588,1059],"class_list":["post-3343","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-alebraic","tag-condition","tag-curve","tag-equation","tag-locus"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3343","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=3343"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3343\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=3343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=3343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=3343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}