Question

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

Answer 1

$❥\huge\underline\mathfrak\purple{Answer}$

$\large{\sf{\fbox{Explanation→}}}$

$\sf{Given,}$

$\sf{When~the~origin~is~shifted~to}$

$\sf{(-1,2)~by~the~translation~of~axes.}$

$\sf{Find~the~transformed~equation~of}$

$\sf{x²+y²+2x-4y+1=10}$

$\red\longrightarrow$ Now old origin is (0,0)

$\red\longrightarrow$ New origin will be (h,k) = (-1,2)

$\red\longrightarrow$ So, = -1, k = 2

$\red\longrightarrow$ Now old coordinates are x, y

$\red\longrightarrow$ New coordinates are x1 y1

$\red\longrightarrow$ Old coordinates=new coordinates+origin

$\red\longrightarrow$ So, we have x = x1 + h and y = y1 + k (Since the origin is shifted from 1,1)

$\red\longrightarrow$ So, x = x1, y = y + 2

$\red\longrightarrow$ So, from the equation we have -

x² + y² + 2x - 4y + 1 = 0

$\red\longrightarrow$ So,(x1-1)²+(y1+2)²+2(x1-1)-4(y1+2)+1=0

$\red\longrightarrow$ Or, x1² - 2x1 + 1 + y1² + 4y1 + 4 + 2x1 - 2 - 4y 1 - 8 + 1 = 0

$\red\longrightarrow$ Or, x1² + y1² - 4 = 0

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Answer 2

Step-by-step explanation:

Given,

When the origin is shifted to

(−1,2) by the translation of axes.

Find the transformed equation of

x²+y²+2x−4y+1=10

⟶ Now old origin is (0,0)

⟶ New origin will be (h,k) = (-1,2)

⟶ So, = -1, k = 2

⟶ Now old coordinates are x, y

⟶ New coordinates are x1 y1

⟶ Old coordinates=new coordinates+origin

⟶ So, we have x = x1 + h and y = y1 + k (Since the origin is shifted from 1,1)

⟶ So, x = x1, y = y + 2

⟶ So, from the equation we have -

x² + y² + 2x - 4y + 1 = 0

⟶ So,(x1-1)²+(y1+2)²+2(x1-1)-4(y1+2)+1=0

⟶ Or, x1² - 2x1 + 1 + y1² + 4y1 + 4 + 2x1 - 2 - 4y 1 - 8 + 1 = 0

⟶ Or, x1² + y1² - 4 = 0

❥itzmisscomplicated4⚡