Defence Exam > Defence Questions > Consider the followingConsider the parabola y...
Start Learning for Free
Consider the following
Consider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .
Q. What are the coordinates of the point on the parabola which is closest to the straight line?
- a)( 0,2 )
- b)(-2 ,-8)
- c)(-7,2)
- d)(1,10)
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider the followingConsider the parabola y = x2 + 7x + 2 and the st...
Parabola Eq : y = x2 + 7x +2
Line eq. :y = 3x - 3
Since all the points given in the options lie on the parabola.
Thus we will calculate the distance from the given line to these points :
Most Upvoted Answer
Consider the followingConsider the parabola y = x2 + 7x + 2 and the st...
Understanding the Problem
To find the closest point on the parabola y = x² + 7x + 2 to the line y = 3x - 3, we can follow these steps:
Step 1: Find the Distance Function
- The distance (D) between a point (x, y) on the parabola and a point (x, 3x - 3) on the line can be expressed as:
- D = √[(x - x)² + (y - (3x - 3))²]
- Since we want to minimize D, we can minimize D² to avoid the square root:
- D² = (y - (3x - 3))²
Step 2: Substitute y from the Parabola
- Replace y in the distance function with the parabola equation:
- D² = (x² + 7x + 2 - (3x - 3))²
- Simplifying gives:
- D² = (x² + 4x + 5)²
Step 3: Minimize D²
- To find the minimum distance, take the derivative of D² with respect to x and set it to zero:
- Find the critical points by solving the equation obtained from the derivative.
Step 4: Identify the Closest Point
- After evaluating the critical points, you will find that the point (-2, -8) on the parabola yields the minimum distance to the line y = 3x - 3.
- Therefore, the closest point is (-2, -8).
Conclusion
- Thus, the coordinates of the point on the parabola which is closest to the straight line are:
- (-2, -8), which corresponds to option 'B'.
To find the closest point on the parabola y = x² + 7x + 2 to the line y = 3x - 3, we can follow these steps:
Step 1: Find the Distance Function
- The distance (D) between a point (x, y) on the parabola and a point (x, 3x - 3) on the line can be expressed as:
- D = √[(x - x)² + (y - (3x - 3))²]
- Since we want to minimize D, we can minimize D² to avoid the square root:
- D² = (y - (3x - 3))²
Step 2: Substitute y from the Parabola
- Replace y in the distance function with the parabola equation:
- D² = (x² + 7x + 2 - (3x - 3))²
- Simplifying gives:
- D² = (x² + 4x + 5)²
Step 3: Minimize D²
- To find the minimum distance, take the derivative of D² with respect to x and set it to zero:
- Find the critical points by solving the equation obtained from the derivative.
Step 4: Identify the Closest Point
- After evaluating the critical points, you will find that the point (-2, -8) on the parabola yields the minimum distance to the line y = 3x - 3.
- Therefore, the closest point is (-2, -8).
Conclusion
- Thus, the coordinates of the point on the parabola which is closest to the straight line are:
- (-2, -8), which corresponds to option 'B'.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer?
Question Description
Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. 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 Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer?.
Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. 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 Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer?.
Solutions for Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. 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 Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the followingConsider the parabola y = x2 + 7x + 2 and the straight line y = 3x - 3 .Q. What are the coordinates of the point on the parabola which is closest to the straight line?a)( 0,2 )b)(-2 ,-8)c)(-7,2)d)(1,10)Correct answer is option 'B'. 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup