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The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0?
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The locus of the center of the circle which bisect the circumference o...
The equation of the circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2.
In this case, we want to find the locus of the centers of the circles that bisect the circumference of the circle x^2 + y^2 = 4.
Let (a, b) be the coordinates of the center of the circle we are looking for. Since the circle bisects the circumference of the circle x^2 + y^2 = 4, the distance from (a, b) to the origin (0, 0) is equal to the radius of the larger circle, which is 2.
Using the distance formula, we have:
√((a-0)^2 + (b-0)^2) = 2
Simplifying this equation, we get:
√(a^2 + b^2) = 2
Squaring both sides, we have:
a^2 + b^2 = 4
This is the equation of a circle centered at the origin (0, 0) with radius 2. Therefore, the locus of the centers of the circles that bisect the circumference of x^2 + y^2 = 4 is the circle x^2 + y^2 = 4.
In this case, we want to find the locus of the centers of the circles that bisect the circumference of the circle x^2 + y^2 = 4.
Let (a, b) be the coordinates of the center of the circle we are looking for. Since the circle bisects the circumference of the circle x^2 + y^2 = 4, the distance from (a, b) to the origin (0, 0) is equal to the radius of the larger circle, which is 2.
Using the distance formula, we have:
√((a-0)^2 + (b-0)^2) = 2
Simplifying this equation, we get:
√(a^2 + b^2) = 2
Squaring both sides, we have:
a^2 + b^2 = 4
This is the equation of a circle centered at the origin (0, 0) with radius 2. Therefore, the locus of the centers of the circles that bisect the circumference of x^2 + y^2 = 4 is the circle x^2 + y^2 = 4.
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The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0?
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The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0?.
The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The locus of the center of the circle which bisect the circumference of the circles x^2 y^2=4 & x^2 y^2-2x 6y 1=0?.
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