JEE Exam > JEE Questions > Let L1 be a straight line through the origin ...
Start Learning for Free
Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.?
Verified Answer
Let L1 be a straight line through the origin and L2 be the straight li...
Let the equation of line L1 be y = mx.
Intercepts made by L1 and L2 on the circle will be equal , i. e, L1 and L2 are at same distance from the centre of the circle.
Centre of the given circle is (1/2, -3/2)
therefore,
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
Let L1 be a straight line through the origin and L2 be the straight li...
To find the intercepts made by the circle on L1, we need to find the points where L1 intersects with the circle.
First, let's find the equation of L1. Since it passes through the origin, its equation can be written as y = mx, where m is the slope of L1.
Next, substitute this equation into the equation of the circle to find the points of intersection:
x^2 + (mx)^2 - x - 3(mx) = 0
Simplifying, we get:
x^2 + m^2x^2 - x - 3mx = 0
Combining like terms, we have:
(1 + m^2)x^2 - (1 + 3m)x = 0
Now, we can find the x-intercepts of this quadratic equation by setting it equal to zero:
(1 + m^2)x^2 - (1 + 3m)x = 0
x((1 + m^2)x - (1 + 3m)) = 0
Either x = 0, or (1 + m^2)x - (1 + 3m) = 0
If x = 0, then y = 0, and this is the origin, which is already given.
If (1 + m^2)x - (1 + 3m) = 0, then x = (1 + 3m)/(1 + m^2)
Substitute this value of x back into the equation of L1 to find the y-coordinate:
y = m * ((1 + 3m)/(1 + m^2))
So, the intercepts made by the circle on L1 are the points ((1 + 3m)/(1 + m^2), m * ((1 + 3m)/(1 + m^2))).
First, let's find the equation of L1. Since it passes through the origin, its equation can be written as y = mx, where m is the slope of L1.
Next, substitute this equation into the equation of the circle to find the points of intersection:
x^2 + (mx)^2 - x - 3(mx) = 0
Simplifying, we get:
x^2 + m^2x^2 - x - 3mx = 0
Combining like terms, we have:
(1 + m^2)x^2 - (1 + 3m)x = 0
Now, we can find the x-intercepts of this quadratic equation by setting it equal to zero:
(1 + m^2)x^2 - (1 + 3m)x = 0
x((1 + m^2)x - (1 + 3m)) = 0
Either x = 0, or (1 + m^2)x - (1 + 3m) = 0
If x = 0, then y = 0, and this is the origin, which is already given.
If (1 + m^2)x - (1 + 3m) = 0, then x = (1 + 3m)/(1 + m^2)
Substitute this value of x back into the equation of L1 to find the y-coordinate:
y = m * ((1 + 3m)/(1 + m^2))
So, the intercepts made by the circle on L1 are the points ((1 + 3m)/(1 + m^2), m * ((1 + 3m)/(1 + m^2))).
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
Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.?
Question Description
Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.?.
Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.?.
Solutions for Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? 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 Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? defined & explained in the simplest way possible. Besides giving the explanation of
Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.?, a detailed solution for Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? has been provided alongside types of Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? theory, EduRev gives you an
ample number of questions to practice Let L1 be a straight line through the origin and L2 be the straight line x y= 1 If the intercepts made by the circle x^2 y^2-x 3y=0 on L1 & L2 are equal, then find the equation(s) which represent L1.? 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
|
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