{"id":20268,"date":"2024-04-15T05:50:38","date_gmt":"2024-04-15T05:50:38","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20268"},"modified":"2024-04-15T05:50:38","modified_gmt":"2024-04-15T05:50:38","slug":"the-angle-of-intersection-of-the-curves-x2-4y-and-y2-4x-at-point-0-0-is-a-0a-b-30a-c-45a-d-90a","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-angle-of-intersection-of-the-curves-x2-4y-and-y2-4x-at-point-0-0-is-a-0a-b-30a-c-45a-d-90a\/","title":{"rendered":"The angle of intersection of the curves x2 = 4y and y2 = 4x at point (0, 0) is A. 0\u00c2\u00b0 B. 30\u00c2\u00b0 C. 45\u00c2\u00b0 D. 90\u00c2\u00b0"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a97dbef19f38\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    0\u00c2\u00b0                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    30\u00c2\u00b0                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    45\u00c2\u00b0                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    90\u00c2\u00b0                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{D}}$.<\/p>\n<p>The angle of intersection of two curves is the angle between their tangent lines at the point of intersection. To find the tangent lines at the point of intersection, we need to find the derivatives of the curves at that point.<\/p>\n<p>The derivatives of $x^2 = 4y$ and $y^2 = 4x$ are $2x = 4y&#8217;$ and $2y = 4x&#8217;$, respectively. Substituting $x = 0$ and $y = 0$ into these equations, we get $2(0) = 4y&#8217;$ and $2(0) = 4x&#8217;$. Solving these equations, we get $y&#8217; = 0$ and $x&#8217; = 0$.<\/p>\n<p>The slopes of the tangent lines are therefore $0$. The angle between two lines with slopes $m_1$ and $m_2$ is given by the formula $\\tan \\theta = \\frac{m_1 &#8211; m_2}{1 + m_1 m_2}$. Substituting $m_1 = 0$ and $m_2 = 0$ into this formula, we get $\\tan \\theta = \\frac{0 &#8211; 0}{1 + 0 \\cdot 0} = 0$. Therefore, the angle of intersection is $\\boxed{90^\\circ}$.<\/p>\n<p>Here is a graph of the two curves:<\/p>\n<p>[asy]<br \/>\nunitsize(1 cm);<\/p>\n<p>draw((0,0)&#8211;(4,4));<br \/>\ndraw((0,0)&#8211;(4,0));<\/p>\n<p>label(&#8220;$x$&#8221;, <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                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you can see, the two curves intersect at a right angle.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The angle of intersection of the curves x2 = 4y and y2 = 4x at point (0, 0) is A. 0\u00c2\u00b0 B. 30\u00c2\u00b0 C. 45\u00c2\u00b0 D. 90\u00c2\u00b0<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-angle-of-intersection-of-the-curves-x2-4y-and-y2-4x-at-point-0-0-is-a-0a-b-30a-c-45a-d-90a\/\" \/>\n<meta property=\"og:locale\" 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