{"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
(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 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> : <\/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> :<\/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> :<\/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> :<\/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\nTypes and Graph of a Parabola :<\/h2>\n