ax+by+c=0 or px+qy+r=0<\/p>\n
So P lies either on ax+by+c=0 or px+qy+r=0 (or both).<\/p>\n
Thus a second degree equation in two variables x<\/em><\/strong> and y<\/em><\/strong> represents a pair of straight lines.<\/p>\n iIf a,b,h are real numbers not all zero, then ax2<\/sup>+2hxy+by2<\/sup>=0 is called homogeneous equation of second degree in x and y and ax2<\/sup>+2hxy+by2<\/sup>+2gx+2fy+c=0 is called the general equation of second degree in x<\/em><\/strong> and y<\/em><\/strong>.<\/p>\n If this general equation of second degree contains a straight line, then this equation can be written as the product of two linear factors in x<\/em><\/strong> and y<\/em><\/strong>.<\/p>\n Thus, if the locus of a second degree equation in x<\/em><\/strong> and y<\/em><\/strong> contains a straight line, then the equation represents a pair of straight lines.\u00a0 If the locus of a second degree equation in two variables x<\/em><\/strong> and y<\/em><\/strong> is a pair of straight lines, then we can write it as (ax+by+c)(px+qy+r)=0 where ax+by+c and px+qy+r are linear in x<\/em><\/strong> and y<\/em><\/strong>.<\/p>\n Note:<\/strong><\/p>\n (1)\u00a0\u00a0\u00a0 The equation ax2<\/sup>+2hxy+by2<\/sup>=0 represents a pair of straight lines if and only if h2<\/sup>\u2265ab.<\/p>\n (2)\u00a0\u00a0\u00a0 If h2<\/sup>=ab, then the lines represented by the equation of locus are coincident.<\/p>\n We also offer Geography tutoring, click here<\/a> for more information.<\/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 Florida visit: Tutoring in Florida. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":" There are several formulae and equations used for the interactions of straight lines. We will explore those below: Consider the equation (ax+by+c)(px+qy+r)=0 which is of second degree equation in two variables x and y. The equations ax+by+c=0 and px+qy+r=0 are linear in x and y and so, either of them represents a straight line. Let […]<\/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":[642,1045,1274,1396,1733],"class_list":["post-5080","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-factor","tag-linear","tag-pair","tag-product","tag-straight-line"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5080","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=5080"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5080\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5080"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5080"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5080"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/11\/pair-of-straight-lines.jpg\" "\\"pair")
<\/a><\/p>\n