{"id":4319,"date":"2022-06-11T07:38:23","date_gmt":"2022-06-11T07:38:23","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4319"},"modified":"2022-06-11T07:38:23","modified_gmt":"2022-06-11T07:38:23","slug":"tangent-and-normal-to-a-curve","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/11\/tangent-and-normal-to-a-curve\/","title":{"rendered":"Tangent and Normal To a Curve"},"content":{"rendered":"\n<p>The equation of tangent and normal line to a curve of a function can be calculated by using the derivatives. If we have a curve of a function and we want to find the equation of the tangent to a curve at a given point, then by using the derivative, we can find the slope and equation of the tangent line. A tangent is a line to a curve that will only touch the curve at a single point and its slope is equal to the derivative of the curve at that point. The slope(m) of the tangent to a curve of a function y = f(x) at a point&nbsp;(x1,y1)(x1,y1)&nbsp;is obtained by taking the derivative of the function (m = f'(x) ).<\/p>\n\n\n\n<p>By finding the\u00a0slope\u00a0of the tangent line to the curve and using the equation\u00a0m=(y\u2212y1)\/(x\u2212x1)m=(y\u2212y1)\/(x\u2212x1), we can find the equation of the tangent line to the curve. Similarly, we can find the equation of the normal line to the curve of a function at a point. This normal line will be normal(perpendicular) to the tangent line. Hence the slope of the normal line to a curve of a function y = f(x) at a point\u00a0(x1,y1)(x1,y1)\u00a0is given as follows.<\/p>\n\n\n\n<p>n = -1\/m = &#8211; 1\/ f'(x)<\/p>\n\n\n\n<p>And by using the equation\u00a0<\/p>\n\n\n\n<p>\u22121\/m = (y\u2212y1) \/ (x\u2212x1)\u22121\/m = (y\u2212y1)\/(x\u2212x1)<\/p>\n\n\n\n<p>\u00a0we can find the equation of the normal line to the curve.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/06\/tangent-and-normal-to-a-curve-1624856731tttttttttttttttt.png\" alt=\"\" class=\"wp-image-4320\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The equation of tangent and normal line to a curve of a function can be calculated by using the derivatives. If we have a curve of a function and we want to find the equation of the tangent to a curve at a given point, then by using the derivative, we can find the slope [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[825],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4319"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4319"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4319\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4319"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4319"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}