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The number of common tangents of the circles x2 + y2 – 2x – 1 = 0 and x2 + y2 – 2y – 7 = 0
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
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The number of common tangents of the circles x2+ y2–2x –1 ...
Internally touch ∴ common tangent is one.
Most Upvoted Answer
The number of common tangents of the circles x2+ y2–2x –1 ...
The equation of a circle centered at the origin with radius r is given by x^2 + y^2 = r^2.
If we have two circles centered at the origin with radii r1 and r2, their equations are x^2 + y^2 = r1^2 and x^2 + y^2 = r2^2, respectively.
To find the common tangents of these two circles, we can solve the system of equations formed by these two equations. Subtracting the second equation from the first, we get:
x^2 + y^2 - (x^2 + y^2) = r1^2 - r2^2
0 = r1^2 - r2^2
This equation simplifies to r1^2 = r2^2, which means that the two radii are equal. Therefore, the two circles are actually the same circle.
Since the two circles are the same, they have an infinite number of common tangents.
If we have two circles centered at the origin with radii r1 and r2, their equations are x^2 + y^2 = r1^2 and x^2 + y^2 = r2^2, respectively.
To find the common tangents of these two circles, we can solve the system of equations formed by these two equations. Subtracting the second equation from the first, we get:
x^2 + y^2 - (x^2 + y^2) = r1^2 - r2^2
0 = r1^2 - r2^2
This equation simplifies to r1^2 = r2^2, which means that the two radii are equal. Therefore, the two circles are actually the same circle.
Since the two circles are the same, they have an infinite number of common tangents.
Community Answer
The number of common tangents of the circles x2+ y2–2x –1 ...
Wrong answer right answer is 4
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The number of common tangents of the circles x2+ y2–2x –1 = 0 and x2+ y2–2y –7 = 0a)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?
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The number of common tangents of the circles x2+ y2–2x –1 = 0 and x2+ y2–2y –7 = 0a)1b)2c)3d)4Correct 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 number of common tangents of the circles x2+ y2–2x –1 = 0 and x2+ y2–2y –7 = 0a)1b)2c)3d)4Correct 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 number of common tangents of the circles x2+ y2–2x –1 = 0 and x2+ y2–2y –7 = 0a)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?.
The number of common tangents of the circles x2+ y2–2x –1 = 0 and x2+ y2–2y –7 = 0a)1b)2c)3d)4Correct 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 number of common tangents of the circles x2+ y2–2x –1 = 0 and x2+ y2–2y –7 = 0a)1b)2c)3d)4Correct 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 number of common tangents of the circles x2+ y2–2x –1 = 0 and x2+ y2–2y –7 = 0a)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?.
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