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The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal to
- a)1/2
- b)1/√2
- c)1/4
- d)√3/2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The circles which can be drawn to pass through (1,0) & (3,0) and t...
Equation of line joining A (1,0) and B (3,0) is y = 0. Equation of family of circles passing through A and B is:
(x – 1)(x – 3) + (y – 0) (y – 0) + λy = 0
x2 + y2 – 4x + λy + 3 = 0
If above circle touches y-axis then x = 0 is a tangent. Substituting x = 0:
y2 + λy + 3 = 0
Discriminant of above quadratic must be zero.
λ2 – 12 = 0
Hence the circles are:
Thus, the coordinates of C1 and C2 are
respectively. Also the radii of each of the circles is r1 = r2 = 2
We know that the angle of intersection of two circles of radii r1 and r2 is given by
where d is the distance between their centers.
Since between two lines whenever there is angle θ there is always the angle π–θ, therefore,
(x – 1)(x – 3) + (y – 0) (y – 0) + λy = 0
x2 + y2 – 4x + λy + 3 = 0
If above circle touches y-axis then x = 0 is a tangent. Substituting x = 0:
y2 + λy + 3 = 0
Discriminant of above quadratic must be zero.
λ2 – 12 = 0
Hence the circles are:
Thus, the coordinates of C1 and C2 are
respectively. Also the radii of each of the circles is r1 = r2 = 2We know that the angle of intersection of two circles of radii r1 and r2 is given by
where d is the distance between their centers.Since between two lines whenever there is angle θ there is always the angle π–θ, therefore,
Most Upvoted Answer
The circles which can be drawn to pass through (1,0) & (3,0) and t...
There are infinitely many circles that can be drawn to pass through the point (1,0).
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The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal toa)1/2b)1/√2c)1/4d)√3/2Correct answer is option 'A'. Can you explain this answer?
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The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal toa)1/2b)1/√2c)1/4d)√3/2Correct answer is option 'A'. 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 The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal toa)1/2b)1/√2c)1/4d)√3/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal toa)1/2b)1/√2c)1/4d)√3/2Correct answer is option 'A'. Can you explain this answer?.
The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal toa)1/2b)1/√2c)1/4d)√3/2Correct answer is option 'A'. 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 The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal toa)1/2b)1/√2c)1/4d)√3/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The circles which can be drawn to pass through (1,0) & (3,0) and touching the y-axis, intersect at an angle θ. The value of cos θ is equal toa)1/2b)1/√2c)1/4d)√3/2Correct answer is option 'A'. Can you explain this answer?.
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