JEE Exam > JEE Questions > The equation of the pair of straight lines pa...
Start Learning for Free
The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2 + y2 - 6x - 4y - 12 = 0 is :
- a)x2 - 4x - 21 = 0
- b)x2 - 5x + 6 = 0
- c)x2 - 6x - 16 = 0
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The equation of the pair of straight lines parallel to the y - axis an...
If a line parallel to y-axis, x = λ touches the given circle, then
Most Upvoted Answer
The equation of the pair of straight lines parallel to the y - axis an...
Problem: Find the equation of the pair of straight lines parallel to the y-axis and which are tangents to the circle x2 + y2 - 6x - 4y - 12 = 0.
Solution:
We know that the equation of a circle with center (a, b) and radius r is (x-a)2 + (y-b)2 = r2.
Here, the given equation is x2 + y2 -6x -4y -12 = 0.
We can rewrite this equation as (x-3)2 + (y-2)2 = 25.
Hence, the center of the circle is (3, 2) and the radius is 5.
Step 1: Find the slope of the tangent to the circle at any point.
To find the slope of the tangent at any point (x1, y1) on the circle, we differentiate the equation of the circle with respect to x as follows:
2(x-3) + 2(y-2) * dy/dx = 0
dy/dx = -(x-3)/(y-2)
Step 2: Find the equations of the tangents that are parallel to the y-axis.
Since the tangents are parallel to the y-axis, their slopes are undefined. This means that (y-2) = 0, or y = 2, for any point of tangency. Therefore, the points of tangency are (3+5, 2) and (3-5, 2), or (8, 2) and (-2, 2).
Step 3: Find the equations of the tangents.
The equations of the tangents passing through (8, 2) and (-2, 2) are:
x = 8 and x = -2
Hence, the equation of the pair of straight lines parallel to the y-axis and which are tangents to the given circle is x = 8 and x = -2, which can be rewritten as follows:
x2 - 6x - 16 = 0 and x2 - 4x - 21 = 0
Therefore, the correct option is (C).
Solution:
We know that the equation of a circle with center (a, b) and radius r is (x-a)2 + (y-b)2 = r2.
Here, the given equation is x2 + y2 -6x -4y -12 = 0.
We can rewrite this equation as (x-3)2 + (y-2)2 = 25.
Hence, the center of the circle is (3, 2) and the radius is 5.
Step 1: Find the slope of the tangent to the circle at any point.
To find the slope of the tangent at any point (x1, y1) on the circle, we differentiate the equation of the circle with respect to x as follows:
2(x-3) + 2(y-2) * dy/dx = 0
dy/dx = -(x-3)/(y-2)
Step 2: Find the equations of the tangents that are parallel to the y-axis.
Since the tangents are parallel to the y-axis, their slopes are undefined. This means that (y-2) = 0, or y = 2, for any point of tangency. Therefore, the points of tangency are (3+5, 2) and (3-5, 2), or (8, 2) and (-2, 2).
Step 3: Find the equations of the tangents.
The equations of the tangents passing through (8, 2) and (-2, 2) are:
x = 8 and x = -2
Hence, the equation of the pair of straight lines parallel to the y-axis and which are tangents to the given circle is x = 8 and x = -2, which can be rewritten as follows:
x2 - 6x - 16 = 0 and x2 - 4x - 21 = 0
Therefore, the correct option is (C).
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer?
Question Description
The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect 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 equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The equation of the pair of straight lines parallel to the y - axis and which are tangents to the circle x2+ y2- 6x - 4y - 12 = 0 is :a)x2- 4x - 21 = 0b)x2- 5x + 6 = 0c)x2- 6x - 16 = 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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