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If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is?
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If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^...
To find the points of intersection between the given circles, we can substitute the equation of the first circle into the second equation and solve for x and y.
Substituting x^2 + y^2 = 4 into the second equation, we get:
(4) - 6x - 8y + 10 = 0
Simplifying, we have:
-6x - 8y + 14 = 0
Dividing by 2, we get:
-3x - 4y + 7 = 0
Now, substitute the equation of the first circle (x^2 + y^2 + 2gx + 2fy + c = 0) into this equation:
(-3x - 4y + 7) + 2gx + 2fy + c = 0
Rearranging, we have:
(2g - 3)x + (2f - 4)y + (c + 7) = 0
Comparing the coefficients of x, y, and the constant term on both sides, we can equate them to find the values of g, f, and c.
For x, we have:
2g - 3 = 0
2g = 3
g = 3/2
For y, we have:
2f - 4 = 0
2f = 4
f = 2
For the constant term, we have:
c + 7 = 0
c = -7
Therefore, the equation of the first circle is:
x^2 + y^2 + 3x + 4y - 7 = 0
Substituting x^2 + y^2 = 4 into the second equation, we get:
(4) - 6x - 8y + 10 = 0
Simplifying, we have:
-6x - 8y + 14 = 0
Dividing by 2, we get:
-3x - 4y + 7 = 0
Now, substitute the equation of the first circle (x^2 + y^2 + 2gx + 2fy + c = 0) into this equation:
(-3x - 4y + 7) + 2gx + 2fy + c = 0
Rearranging, we have:
(2g - 3)x + (2f - 4)y + (c + 7) = 0
Comparing the coefficients of x, y, and the constant term on both sides, we can equate them to find the values of g, f, and c.
For x, we have:
2g - 3 = 0
2g = 3
g = 3/2
For y, we have:
2f - 4 = 0
2f = 4
f = 2
For the constant term, we have:
c + 7 = 0
c = -7
Therefore, the equation of the first circle is:
x^2 + y^2 + 3x + 4y - 7 = 0
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If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is?
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If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is?.
If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a circle x^2 y^2 2gx 2fy c=0 cuts each of the circles x^2 y^2=4, x^2 y^2--6x--8y 10=0 & x^2 y^2 2x--4y--2=0 at the extremities of a diameter then it's centre is?.
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