Question

12.
When the origin is shifted to (-1,2) by the translation of axes,
find the transformed equation of x² + y2 + 2x – 4y +1=0.
Show that the lines
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Answer 1

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=0.

• Now old origin is (0,0)
• New origin will be (h,k) = (-1,2)
• So h = -1 , k = 2
• Now old coordinates is x,y
• New coordinates is x1y1
• Old coordinates = new coordinates + origin
• So we have x = x1 + h and y = y1 + k (Since origin is shifted from 1,1 )
• So x = x1 – 1, y = y’ + 2
• So from the equation we have
• So x^2 + y^2 + 2x – 4y + 1 = 0
• So (x1-1)^2 + (y1 + 2)^2 + 2 (x1 – 1) – 4(y1 + 2) + 1 = 0
• Or x1^2 – 2x1 + 1 + y1^2 + 4y1 + 4 + 2x1 – 2 – 4y1 – 8 + 1 = 0
• Or x1^2 + y1^2 – 4 = 0
• New equation will be x1^2 + y1^2 – 4 = 0

Reference link will be

https://brainly.in/question/19844946

Answer 2

Hope it helps you guyz