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The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:
- a)(11, – 2)
- b)(-2, 11)
- c)(11, 2)
- d)(2, 11)
Correct answer is option 'C'. Can you explain this answer?
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The coordinates of the centre of a circle passing through (1, 2), (3, ...
4), and (5, 6) can be found by solving the system of equations:
(x - 3)^2 + (y - 4)^2 = r^2
(x - 1)^2 + (y - 2)^2 = r^2
(x - 5)^2 + (y - 6)^2 = r^2
where (x, y) are the coordinates of the centre and r is the radius of the circle.
Expanding the first two equations gives:
x^2 - 6x + 9 + y^2 - 8y + 16 = r^2
x^2 - 2x + 1 + y^2 - 4y + 4 = r^2
Subtracting the second equation from the first, we get:
-4x + 4y + 10 = 0
=> x - y = -2.5
Similarly, subtracting the third equation from the first, we get:
-4x + 4y - 10 = 0
=> x - y = 2.5
Solving these two equations simultaneously, we get:
x = 0.5, y = 3
Therefore, the centre of the circle is (0.5, 3).
(x - 3)^2 + (y - 4)^2 = r^2
(x - 1)^2 + (y - 2)^2 = r^2
(x - 5)^2 + (y - 6)^2 = r^2
where (x, y) are the coordinates of the centre and r is the radius of the circle.
Expanding the first two equations gives:
x^2 - 6x + 9 + y^2 - 8y + 16 = r^2
x^2 - 2x + 1 + y^2 - 4y + 4 = r^2
Subtracting the second equation from the first, we get:
-4x + 4y + 10 = 0
=> x - y = -2.5
Similarly, subtracting the third equation from the first, we get:
-4x + 4y - 10 = 0
=> x - y = 2.5
Solving these two equations simultaneously, we get:
x = 0.5, y = 3
Therefore, the centre of the circle is (0.5, 3).
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The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:a)(11, – 2)b)(-2, 11)c)(11, 2)d)(2, 11)Correct answer is option 'C'. Can you explain this answer?
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The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:a)(11, – 2)b)(-2, 11)c)(11, 2)d)(2, 11)Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:a)(11, – 2)b)(-2, 11)c)(11, 2)d)(2, 11)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:a)(11, – 2)b)(-2, 11)c)(11, 2)d)(2, 11)Correct answer is option 'C'. Can you explain this answer?.
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