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Consider a circle passing through the origin and the points (a, b) and (-b, -a).
Q. On which line does the centre of the circle lie?
- a)x + y = 0
- b)x - y = 0
- c)x + y = a + b
- d)x - y = a2 - b2
Correct answer is option 'A'. Can you explain this answer?
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Consider a circle passing through the origin and the points (a, b) and...
Suppose; x2 + y2 + 2gx + 2fy + c = 0 is the eq. of the circle.
Since; it passes through
x + y =0 is the line which passes through (f, -f)
Since; it passes through
x + y =0 is the line which passes through (f, -f)
Most Upvoted Answer
Consider a circle passing through the origin and the points (a, b) and...
To determine the line on which the center of the circle lies, we need to find the equation of the circle passing through the origin and the points (a, b) and (-b, -a).
Let's consider the center of the circle as (h, k) and the radius as r. Since the circle passes through the origin (0, 0), the distance between the center and the origin is equal to the radius, i.e., √(h^2 + k^2) = r.
We can use the midpoint formula to find the coordinates of the center. The midpoint of the line segment joining (a, b) and (-b, -a) is given by the average of their x-coordinates and y-coordinates, which gives us the center as ((a - b)/2, (b - a)/2).
Since the center lies on the line passing through the origin and the points (a, b) and (-b, -a), we can substitute the coordinates of the center into the equation of the line to check the validity.
Let's substitute ((a - b)/2, (b - a)/2) into the equation of the line and simplify:
x - y = 0
((a - b)/2) - ((b - a)/2) = 0
(a - b - b + a)/2 = 0
(2a - 2b)/2 = 0
(a - b) = 0
We can see that (a - b) = 0, which means that the equation of the line is satisfied by the coordinates of the center.
Hence, the correct answer is option A: x - y = 0. The center of the circle lies on the line x - y = 0.
Let's consider the center of the circle as (h, k) and the radius as r. Since the circle passes through the origin (0, 0), the distance between the center and the origin is equal to the radius, i.e., √(h^2 + k^2) = r.
We can use the midpoint formula to find the coordinates of the center. The midpoint of the line segment joining (a, b) and (-b, -a) is given by the average of their x-coordinates and y-coordinates, which gives us the center as ((a - b)/2, (b - a)/2).
Since the center lies on the line passing through the origin and the points (a, b) and (-b, -a), we can substitute the coordinates of the center into the equation of the line to check the validity.
Let's substitute ((a - b)/2, (b - a)/2) into the equation of the line and simplify:
x - y = 0
((a - b)/2) - ((b - a)/2) = 0
(a - b - b + a)/2 = 0
(2a - 2b)/2 = 0
(a - b) = 0
We can see that (a - b) = 0, which means that the equation of the line is satisfied by the coordinates of the center.
Hence, the correct answer is option A: x - y = 0. The center of the circle lies on the line x - y = 0.
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Consider a circle passing through the origin and the points (a, b) and (-b, -a).Q. On which line does the centre of the circle lie?a)x + y = 0b)x - y = 0c)x + y = a + bd)x - y = a2 - b2Correct answer is option 'A'. Can you explain this answer?
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Consider a circle passing through the origin and the points (a, b) and (-b, -a).Q. On which line does the centre of the circle lie?a)x + y = 0b)x - y = 0c)x + y = a + bd)x - y = a2 - b2Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider a circle passing through the origin and the points (a, b) and (-b, -a).Q. On which line does the centre of the circle lie?a)x + y = 0b)x - y = 0c)x + y = a + bd)x - y = a2 - b2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a circle passing through the origin and the points (a, b) and (-b, -a).Q. On which line does the centre of the circle lie?a)x + y = 0b)x - y = 0c)x + y = a + bd)x - y = a2 - b2Correct answer is option 'A'. Can you explain this answer?.
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