Defence Exam > Defence Questions > The line 2y = 3x + 12 cuts the parabola 4y = ...
Start Learning for Free
The line 2y = 3x + 12 cuts the parabola 4y = 3x2.
What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?
- a)7 square unit
- b)14 square unit
- c)20 square unit
- d)21 square unit
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area encl...
Equation of line 2y = 3x + 12 and equations of parabola 4y=3x2
= 3 x 4 + 24 - 16 = 36 - 16 = 20 sq. units.
∴Area enclosed by the parabola, the line and the y axis in first quadrant = 20 sq. units
= 3 x 4 + 24 - 16 = 36 - 16 = 20 sq. units.
∴Area enclosed by the parabola, the line and the y axis in first quadrant = 20 sq. units
Most Upvoted Answer
The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area encl...
Given:
Equation of the line: 2y = 3x - 12
Equation of the parabola: 4y = 3x^2
To find the area enclosed by the parabola, line, and y-axis in the first quadrant, we need to find the points of intersection of the line and the parabola.
Step 1: Find the points of intersection
To find the points of intersection, we can equate the two equations:
3x - 12 = 3x^2/2
Rearranging the terms, we get:
3x^2 - 6x - 24 = 0
Dividing by 3, we get:
x^2 - 2x - 8 = 0
Factoring the quadratic equation, we get:
(x - 4)(x + 2) = 0
So, x = 4 or x = -2
Substituting the values of x back into the equation of the line, we get the corresponding y-values:
For x = 4, 2y = 3(4) - 12
2y = 12 - 12
2y = 0
y = 0
For x = -2, 2y = 3(-2) - 12
2y = -6 - 12
2y = -18
y = -9
Since we are looking for the intersection points in the first quadrant, we discard the point (-2, -9) as it lies in the third quadrant.
Step 2: Find the area enclosed
Now that we have the points of intersection, we can find the area enclosed by calculating the area under the parabola and subtracting the area under the line.
Using integration, we can find the area under the parabola:
∫[0,4] 4y/3 dx = (∫[0,4] 4/3)∫y dx = 4/3 * (∫[0,4] dx)
= 4/3 * [x] [0,4]
= 4/3 * (4 - 0)
= 16/3
Using integration, we can find the area under the line:
∫[0,4] (3x - 12)/2 dy = (∫[0,4] (3x - 12)/2)∫dx = 1/2 * (∫[0,4] 3x - 12) dx
= 1/2 * [(3/2)x^2 - 12x] [0,4]
= 1/2 * [(3/2)(4)^2 - 12(4) - (3/2)(0)^2 - 12(0)]
= 1/2 * [(3/2)(16) - 48 - (3/2)(0) - 0]
= 1/2 * [24 - 48]
= 1/2 * (-24)
= -12
Therefore, the area enclosed by the parabola, line, and y-axis in the first quadrant is:
Area = (16/3) - (-12)
= 16/3 + 12/1
= 64/3 + 36/3
= 100
Equation of the line: 2y = 3x - 12
Equation of the parabola: 4y = 3x^2
To find the area enclosed by the parabola, line, and y-axis in the first quadrant, we need to find the points of intersection of the line and the parabola.
Step 1: Find the points of intersection
To find the points of intersection, we can equate the two equations:
3x - 12 = 3x^2/2
Rearranging the terms, we get:
3x^2 - 6x - 24 = 0
Dividing by 3, we get:
x^2 - 2x - 8 = 0
Factoring the quadratic equation, we get:
(x - 4)(x + 2) = 0
So, x = 4 or x = -2
Substituting the values of x back into the equation of the line, we get the corresponding y-values:
For x = 4, 2y = 3(4) - 12
2y = 12 - 12
2y = 0
y = 0
For x = -2, 2y = 3(-2) - 12
2y = -6 - 12
2y = -18
y = -9
Since we are looking for the intersection points in the first quadrant, we discard the point (-2, -9) as it lies in the third quadrant.
Step 2: Find the area enclosed
Now that we have the points of intersection, we can find the area enclosed by calculating the area under the parabola and subtracting the area under the line.
Using integration, we can find the area under the parabola:
∫[0,4] 4y/3 dx = (∫[0,4] 4/3)∫y dx = 4/3 * (∫[0,4] dx)
= 4/3 * [x] [0,4]
= 4/3 * (4 - 0)
= 16/3
Using integration, we can find the area under the line:
∫[0,4] (3x - 12)/2 dy = (∫[0,4] (3x - 12)/2)∫dx = 1/2 * (∫[0,4] 3x - 12) dx
= 1/2 * [(3/2)x^2 - 12x] [0,4]
= 1/2 * [(3/2)(4)^2 - 12(4) - (3/2)(0)^2 - 12(0)]
= 1/2 * [(3/2)(16) - 48 - (3/2)(0) - 0]
= 1/2 * [24 - 48]
= 1/2 * (-24)
= -12
Therefore, the area enclosed by the parabola, line, and y-axis in the first quadrant is:
Area = (16/3) - (-12)
= 16/3 + 12/1
= 64/3 + 36/3
= 100
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer?
Question Description
The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer?.
The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The line 2y = 3x + 12 cuts the parabola 4y = 3x2.What is the area enclosed by the parabola, the line and the Y- axis in the first quadrant ?a)7 square unitb)14 square unitc)20 square unitd)21 square unitCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup