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Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12?
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Obtain the equation of the circle whose centre is (4,5) and whose circ...
Given:
- Centre of the circle: (4, 5)
- Equation of the circle: x^2 + y^2 + 4x - 6y = 12
Step 1: Identify the coordinates of the center of the circle.
The given equation of the circle is in the general form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center and r represents the radius. Comparing this with the given equation, we can identify the center of the circle as (h, k) = (-2, 3).
Step 2: Find the radius of the circle.
To find the radius of the circle, we can use the formula r = √((x - h)^2 + (y - k)^2), where (x, y) represents any point on the circle. Since the center of the circle is (-2, 3), we can choose this point to calculate the radius. Plugging in the values, we get r = √((-2 - 4)^2 + (3 - 5)^2) = √(36 + 4) = √40 = 2√10.
Step 3: Write the equation of the circle.
Now that we have the center and radius of the circle, we can write the equation in the form (x - h)^2 + (y - k)^2 = r^2. Substituting the values, we get (x + 2)^2 + (y - 3)^2 = (2√10)^2 = 40.
Conclusion:
The equation of the circle with center (4, 5) and circumference passing through the center of the circle x^2 + y^2 + 4x - 6y = 12 is (x + 2)^2 + (y - 3)^2 = 40.
- Centre of the circle: (4, 5)
- Equation of the circle: x^2 + y^2 + 4x - 6y = 12
Step 1: Identify the coordinates of the center of the circle.
The given equation of the circle is in the general form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center and r represents the radius. Comparing this with the given equation, we can identify the center of the circle as (h, k) = (-2, 3).
Step 2: Find the radius of the circle.
To find the radius of the circle, we can use the formula r = √((x - h)^2 + (y - k)^2), where (x, y) represents any point on the circle. Since the center of the circle is (-2, 3), we can choose this point to calculate the radius. Plugging in the values, we get r = √((-2 - 4)^2 + (3 - 5)^2) = √(36 + 4) = √40 = 2√10.
Step 3: Write the equation of the circle.
Now that we have the center and radius of the circle, we can write the equation in the form (x - h)^2 + (y - k)^2 = r^2. Substituting the values, we get (x + 2)^2 + (y - 3)^2 = (2√10)^2 = 40.
Conclusion:
The equation of the circle with center (4, 5) and circumference passing through the center of the circle x^2 + y^2 + 4x - 6y = 12 is (x + 2)^2 + (y - 3)^2 = 40.
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Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12?
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Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12?.
Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Obtain the equation of the circle whose centre is (4,5) and whose circumference passes through the center of the circle x2 y2 4x-6y=12?.
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