Question

find the transformed equation of x^2+y^2+2x-4y+1=0 when the origin is shifted to the point (-1,2) ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

Let the origin is shifted to the point ( h, k)

So that a point ( x, y) in old system transformed into (x', y') such that

$x = x' + h \: , \:y = y' + k$

TO DETERMINE

The transformed equation of

${x}^{2} + {y}^{2} + 2x - 4y + 1 = 0$

when the origin is shifted to the point (-1,2)

EVALUATION

Here the origin is shifted to the point ( - 1 , 2)

) So that a point ( x, y) in old system transformed into (x', y') such that

$x = x' - 1 \: , \:y = y' + 2$

The given equation

${x}^{2} + {y}^{2} + 2x - 4y + 1 = 0$

Can be rewritten as

${(x + 1)}^{2} + {(y - 2)}^{2} = 4$

So the transformed equation is

${(x' - 1 + 1)}^{2} + {(y' + 2- 2)}^{2} = 4$

$\implies \: {(x' )}^{2} + {(y' )}^{2} = 4$

RESULT

THE REQUIRED EQUATION IS

$\boxed{ \: \: {(x' )}^{2} + {(y' )}^{2} = 4 \: }$

Answer 2

Answer:

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