{"id":2429,"date":"2021-07-08T17:28:23","date_gmt":"2021-07-08T17:28:23","guid":{"rendered":"https:\/\/mathemerize.com\/?p=2429"},"modified":"2021-11-27T18:08:49","modified_gmt":"2021-11-27T12:38:49","slug":"graph-of-a-parabola","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/graph-of-a-parabola\/","title":{"rendered":"Graph of a Parabola – Types of Parabolas"},"content":{"rendered":"

A parabola is locus of a point which moves in a plane, such that its distance from a fixed point called focus is equal to its perpendicular distance from a fixed straight line called directrix. Graph of a Parabola and their types are shown below.<\/p>\n

Basic Concepts of a Parabola<\/h2>\n

(a) Focal distance :<\/strong> The distance of a point on parabola from the focus is called focal distance of the point.<\/p>\n

(b) Focal chord : <\/strong>A chord of parabola, which passes through focus is called focal chord.<\/p>\n

(c) Double ordinate : <\/strong>A chord of the parabola perpendicular to the axis of the symmetry is called double ordinate.<\/p>\n

(d) Latus rectum : <\/strong>A double ordinate passing through focus or a focal chord perpendicular to axis of parabola is called latus rectum.<\/p>\n

Types and Graph of a Parabola :<\/h2>\n

Four standard forms of parabola are \\(y^2\\) = 4ax ; \\(y^2\\) = -4ax ; \\(x^2\\) = 4ay ; \\(x^2\\) = -4ay. All of them with their graphs are given below :<\/p>\n

(i) Parabola \\(y^2 = 4ax\\)<\/strong> : \"y2<\/p>\n

Vertex O is (0, 0)<\/p>\n

Focus S is (a, 0)<\/p>\n

Axis is y = 0<\/p>\n

Directrix ZZ’ is x = -a<\/p>\n

Focal length = x + a<\/p>\n

Length of Latus rectum = 4a<\/p>\n

(ii) Parabola \\(y^2 = -4ax\\)<\/strong> :\"y2<\/p>\n

Vertex O is (0,0)<\/p>\n

Focus S is (-a,0)<\/p>\n

Axis is y = 0<\/p>\n

Directrix ZZ’ is x = a<\/p>\n

Focal length = x – a<\/p>\n

Length of Latus rectum = 4a<\/p>\n

(iii) Parabola \\(x^2 = 4ay\\)<\/strong> :\"x2<\/p>\n

Vertex O is (0,0)<\/p>\n

Focus S is (0,a)<\/p>\n

Axis is x = 0<\/p>\n

Directrix ZZ’ is y = -a<\/p>\n

Focal length = y + a<\/p>\n

Length of Latus rectum = 4a<\/p>\n

(iv) Parabola \\(x^2 = -4ay\\)<\/strong> :\"x2<\/p>\n

Vertex O is (0,0)<\/p>\n

Focus S is (0,-a)<\/p>\n

Axis is x = 0<\/p>\n

Directrix ZZ’ is y = a<\/p>\n

Focal length = y – a<\/p>\n

Length of Latus rectum = 4a<\/p>\n

Hope you learnt basic concepts and graph of a parabola, learn more concepts of parabola and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n

\n
Next – Different Types of Parabola Equations<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Formulas for Conic Sections \u2013 Equations & Concepts<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

A parabola is locus of a point which moves in a plane, such that its distance from a fixed point called focus is equal to its perpendicular distance from a fixed straight line called directrix. Graph of a Parabola and their types are shown below. Basic Concepts of a Parabola (a) Focal distance : The …<\/p>\n

Graph of a Parabola – Types of Parabolas<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[12],"tags":[516,513,517,512],"yoast_head":"\nGraph of a Parabola - Types of Parabolas - Mathemerize<\/title>\n<meta name=\"description\" content=\"Learn what is parabola and four types of parabolas, basic concepts of parabola and graph of a parabola here.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/graph-of-a-parabola\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Graph of a Parabola - 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