JEE Exam > JEE Questions > Lines x2+4xy+y2=0 and x-y=4 form the figurea)...
Start Learning for Free
Lines x2+4xy+y2=0 and x-y=4 form the figure
- a)a right angle triangle
- b)an isosceles triangle
- c)an equilateral triangle
- d)scalane triangle
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)a...
Solution:
Given equation of lines are x^2 + 2xy + y^2 = 0, and x - y = 4.
Let's solve the equation of given lines:
x^2 + 2xy + y^2 = 0
Adding x^2 and y^2 on both sides, we get:
x^2 + 2xy + y^2 + x^2 + y^2 = x^2 + y^2
2(x^2 + xy + y^2) = x^2 + y^2
x^2 + y^2 = 2xy
Now, solving this equation with the equation x - y = 4, we get:
x^2 + y^2 = 2xy
(x - y)^2 = 4^2
(x - y) = ±4
Now, we have two cases to consider:
Case 1: x - y = 4
Substituting this value in the equation x^2 + y^2 = 2xy, we get:
x^2 + y^2 = 2xy
(x - y)^2 + 2xy = 2xy
(x - y)^2 = 0
x = y
Hence, the equation of the line becomes x - x = 4, which is not possible.
Therefore, this case is not possible.
Case 2: x - y = -4
Substituting this value in the equation x^2 + y^2 = 2xy, we get:
x^2 + y^2 = 2xy
(x - y)^2 + 2xy = 2xy
(x - y)^2 = 0
x = y
Hence, the equation of the line becomes x - x = -4, which is not possible.
Therefore, this case is also not possible.
Hence, the given lines do not intersect each other.
Therefore, the figure formed by these lines is not a triangle.
Hence, the answer is none of the above options.
Given equation of lines are x^2 + 2xy + y^2 = 0, and x - y = 4.
Let's solve the equation of given lines:
x^2 + 2xy + y^2 = 0
Adding x^2 and y^2 on both sides, we get:
x^2 + 2xy + y^2 + x^2 + y^2 = x^2 + y^2
2(x^2 + xy + y^2) = x^2 + y^2
x^2 + y^2 = 2xy
Now, solving this equation with the equation x - y = 4, we get:
x^2 + y^2 = 2xy
(x - y)^2 = 4^2
(x - y) = ±4
Now, we have two cases to consider:
Case 1: x - y = 4
Substituting this value in the equation x^2 + y^2 = 2xy, we get:
x^2 + y^2 = 2xy
(x - y)^2 + 2xy = 2xy
(x - y)^2 = 0
x = y
Hence, the equation of the line becomes x - x = 4, which is not possible.
Therefore, this case is not possible.
Case 2: x - y = -4
Substituting this value in the equation x^2 + y^2 = 2xy, we get:
x^2 + y^2 = 2xy
(x - y)^2 + 2xy = 2xy
(x - y)^2 = 0
x = y
Hence, the equation of the line becomes x - x = -4, which is not possible.
Therefore, this case is also not possible.
Hence, the given lines do not intersect each other.
Therefore, the figure formed by these lines is not a triangle.
Hence, the answer is none of the above options.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer?
Question Description
Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer?.
Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect 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 Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Lines x2+4xy+y2=0 and x-y=4 form the figurea)a right angle triangleb)an isosceles trianglec)an equilateral triangled)scalane triangleCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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