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If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is?
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If the transformed equation of a curve when the origin is translated t...
Transformation of Equation
- The given transformed equation is X^2 + Y^2 + 2X - Y + 2 = 0 after translating the origin to (1,1).
- To find the original equation, we need to reverse the translation. This can be done by substituting X = x+1 and Y = y+1 into the transformed equation.
Substitution
- Substituting X = x+1 and Y = y+1 into X^2 + Y^2 + 2X - Y + 2 = 0, we get:
- (x+1)^2 + (y+1)^2 + 2(x+1) - (y+1) + 2 = 0
- Simplifying the above equation gives the original equation of the curve.
Original Equation
- Expanding the terms and simplifying further, we get:
- x^2 + y^2 + 2x - y = 0
- Therefore, the original equation of the curve before the translation is x^2 + y^2 + 2x - y = 0.
- The given transformed equation is X^2 + Y^2 + 2X - Y + 2 = 0 after translating the origin to (1,1).
- To find the original equation, we need to reverse the translation. This can be done by substituting X = x+1 and Y = y+1 into the transformed equation.
Substitution
- Substituting X = x+1 and Y = y+1 into X^2 + Y^2 + 2X - Y + 2 = 0, we get:
- (x+1)^2 + (y+1)^2 + 2(x+1) - (y+1) + 2 = 0
- Simplifying the above equation gives the original equation of the curve.
Original Equation
- Expanding the terms and simplifying further, we get:
- x^2 + y^2 + 2x - y = 0
- Therefore, the original equation of the curve before the translation is x^2 + y^2 + 2x - y = 0.
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If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is?
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If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is?.
If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the transformed equation of a curve when the origin is translated to (1,1)is X^2+Y^2+2X-Y+2=0 then the original equation of the curve is?.
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