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What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).?
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What does the equation x2 y2-4x-6y 11=0 become, when the origin is shi...
When origin is shifted to the point (1,1), then
Substituting the above value in the given equation, we get
Thus, new equation of the curve will be
Note- When the origin is shifted to the point (h,k) without changing the direction of axes, new equation of the curve can be directly obtained by putting (x+h) in place of x and (y+k) in place of y in the given equation of the curve.
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What does the equation x2 y2-4x-6y 11=0 become, when the origin is shi...
Shifting the Origin to (1,1)
When the origin is shifted to the point (1,1), we need to make a change of variables to adjust the equation. Let's denote the new coordinates as (x',y'), then the relationship between the old and new coordinates is given by:
x = x' + 1
y = y' + 1
Substitute the new coordinates
Substitute the new coordinates into the original equation x^2 y^2 - 4x - 6y + 11 = 0:
(x' + 1)^2 (y' + 1)^2 - 4(x' + 1) - 6(y' + 1) + 11 = 0
Expanding and simplifying this equation will give the transformed equation in terms of x' and y'.
Expand and simplify
(x'^2 + 2x' + 1)(y'^2 + 2y' + 1) - 4x' - 4 - 6y' - 6 + 11 = 0
x'^2 y'^2 + 2x'y'^2 + x'^2 + 2x'y' + 4x' + y'^2 + 2y' + 1 - 4x' - 4 - 6y' - 6 + 11 = 0
x'^2 y'^2 + 2x'y'^2 + y'^2 + 2x'y' - 2x' - 6y' + 2 = 0
Final Equation
Therefore, the equation x'^2 y'^2 + 2x'y'^2 + y'^2 + 2x'y' - 2x' - 6y' + 2 = 0 is the transformed equation after shifting the origin to the point (1,1). This new equation represents the same curve as the original equation but with the origin now located at (1,1).
When the origin is shifted to the point (1,1), we need to make a change of variables to adjust the equation. Let's denote the new coordinates as (x',y'), then the relationship between the old and new coordinates is given by:
x = x' + 1
y = y' + 1
Substitute the new coordinates
Substitute the new coordinates into the original equation x^2 y^2 - 4x - 6y + 11 = 0:
(x' + 1)^2 (y' + 1)^2 - 4(x' + 1) - 6(y' + 1) + 11 = 0
Expanding and simplifying this equation will give the transformed equation in terms of x' and y'.
Expand and simplify
(x'^2 + 2x' + 1)(y'^2 + 2y' + 1) - 4x' - 4 - 6y' - 6 + 11 = 0
x'^2 y'^2 + 2x'y'^2 + x'^2 + 2x'y' + 4x' + y'^2 + 2y' + 1 - 4x' - 4 - 6y' - 6 + 11 = 0
x'^2 y'^2 + 2x'y'^2 + y'^2 + 2x'y' - 2x' - 6y' + 2 = 0
Final Equation
Therefore, the equation x'^2 y'^2 + 2x'y'^2 + y'^2 + 2x'y' - 2x' - 6y' + 2 = 0 is the transformed equation after shifting the origin to the point (1,1). This new equation represents the same curve as the original equation but with the origin now located at (1,1).
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What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).?
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What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).? 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 What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).?.
What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).? 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 What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What does the equation x2 y2-4x-6y 11=0 become, when the origin is shifted to the point (1,1).?.
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