The Parabolas Y2 = 4x And X2 = 4y Divide The Square ... - EduRev

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Less EduRev Explore Exams Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for FreeSign in Open App JEE Exam > JEE Questions > The parabolas y2 = 4x and x2 = 4y divide the ... Start Learning for Free The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ is
  • a)1 : 2 : 3
  • b)1 : 2 : 1
  • c)1 : 1 : 1
  • d)2 : 1: 2
Correct answer is option 'C'. Can you explain this answer?
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Verified AnswerThe parabolas y2 = 4x and x2 = 4y divide the square region bounded by ...View all questions of this testMost Upvoted AnswerThe parabolas y2 = 4x and x2 = 4y divide the square region bounded by ...Answered by Learners Habitat · View profileFree Test
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View all free JEE testsCommunity AnswerThe parabolas y2 = 4x and x2 = 4y divide the square region bounded by ...Given parabolas: y^2 = 4x and x^2 = 4yRegion bounded by the lines x = 4, y = 4 and the coordinate axesTo find the areas of the different parts of the region, we need to find the points of intersection of the parabolas.To find the intersection points, we can equate the two equations:4x = x^2=> x^2 - 4x = 0=> x(x - 4) = 0So, there are two intersection points: (0,0) and (4,4).Now, we can divide the region into three parts based on the parabolas and the coordinate axes.Part 1: Area above y^2 = 4x and below x = 4The parabola y^2 = 4x is symmetric about the y-axis. So, we can consider only the part of the parabola in the first quadrant.To find the area above y^2 = 4x and below x = 4, we need to find the area between the x-axis and the parabola y^2 = 4x from x = 0 to x = 4.The equation of the parabola can be written as y = √(4x).So, the area of this part can be found by integrating the function y = √(4x) with respect to x from 0 to 4.∫[0,4] √(4x) dx = [2/3 * (4x)^(3/2)] [0,4] = 2/3 * (4^2)^(3/2) = 2/3 * 8^(3/2) = 2/3 * 8 * 2 = 32/3Part 2: Area above x^2 = 4y and below y = 4The parabola x^2 = 4y is symmetric about the x-axis. So, we can consider only the part of the parabola in the first quadrant.To find the area above x^2 = 4y and below y = 4, we need to find the area between the y-axis and the parabola x^2 = 4y from y = 0 to y = 4.The equation of the parabola can be written as x = √(4y).So, the area of this part can be found by integrating the function x = √(4y) with respect to y from 0 to 4.∫[0,4] √(4y) dy = [2/3 * (4y)^(3/2)] [0,4] = 2/3 * (4^2)^(3/2) = 2/3 * 8^(3/2) = 2/3 * 8 * 2 = 32/3Part 3: Area between the parabolas y^2 = 4x and x^2 = 4yTo find the area between the parabolas y^2 = 4x and x^2 = 4y, we need to find the area between the curves y = √(4x) andShare your AnswerView all answers
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View all Question Description The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer?.Solutions for The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.Here you can find the meaning of The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ isa)1 : 2 : 3b)1 : 2 : 1c)1 : 1 : 1d)2 : 1: 2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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