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The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is
- a)[(3/2), (1/2)]
- b)[(1/2), (3/2)]
- c)[(1/2), (1/2)]
- d)[(1/2), - √2]
Correct answer is option 'D'. Can you explain this answer?
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The centre of a circle passing through the points (0, 0), (1, 0) and t...
Given Information:
- The circle passes through the points (0, 0) and (1, 0).
- The circle touches the circle x^2 + y^2 = 9.
Solution:
Finding the Equation of the Circle Passing Through (0, 0) and (1, 0):
- The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
- Plugging in the points (0, 0) and (1, 0) into the general equation, we get the equation of the circle passing through these points as x^2 + y^2 - 2hx = 0.
- Substituting the coordinates of the points (1, 0) and (0, 0) into the equation, we get h = 1/2.
Finding the Equation of the Circle Touching x^2 + y^2 = 9:
- The equation of the circle x^2 + y^2 = 9 is a circle with center at the origin and radius 3.
Center of the Circle Passing Through (0, 0) and (1, 0) and Touching x^2 + y^2 = 9:
- Since the circle touches x^2 + y^2 = 9, the distance between the center of the circle passing through (0, 0) and (1, 0) and the center of x^2 + y^2 = 9 should be equal to 3.
- The center of the circle passing through (0, 0) and (1, 0) is at a distance of 1/2 units from the x-axis.
- Therefore, the center of the circle is at a distance of 3 units from the origin along the x-axis.
- Hence, the center of the circle passing through (0, 0) and (1, 0) and touching x^2 + y^2 = 9 is (1/2, -√2).
Therefore, the correct answer is option 'D'.
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The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2= 9 isa)[(3/2), (1/2)]b)[(1/2), (3/2)]c)[(1/2), (1/2)]d)[(1/2), - √2]Correct answer is option 'D'. Can you explain this answer?
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The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2= 9 isa)[(3/2), (1/2)]b)[(1/2), (3/2)]c)[(1/2), (1/2)]d)[(1/2), - √2]Correct answer is option 'D'. 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 centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2= 9 isa)[(3/2), (1/2)]b)[(1/2), (3/2)]c)[(1/2), (1/2)]d)[(1/2), - √2]Correct answer is option 'D'. 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 centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2= 9 isa)[(3/2), (1/2)]b)[(1/2), (3/2)]c)[(1/2), (1/2)]d)[(1/2), - √2]Correct answer is option 'D'. Can you explain this answer?.
The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2= 9 isa)[(3/2), (1/2)]b)[(1/2), (3/2)]c)[(1/2), (1/2)]d)[(1/2), - √2]Correct answer is option 'D'. 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 centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2= 9 isa)[(3/2), (1/2)]b)[(1/2), (3/2)]c)[(1/2), (1/2)]d)[(1/2), - √2]Correct answer is option 'D'. 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 centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2= 9 isa)[(3/2), (1/2)]b)[(1/2), (3/2)]c)[(1/2), (1/2)]d)[(1/2), - √2]Correct answer is option 'D'. Can you explain this answer?.
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