Question

When the origin is shifted to (-1, 2) by the translation
of axes,
find the transformed equation of the following x²+ y² + 2x-4y+1 = 0​

Answer 1

Answer:

The given equation is x^{2}+y^{2}+2x - 4y+1 = 0x

2

+y

2

+2x−4y+1=0

We take the new origin (h,k)(h,k) as (-1,2)(−1,2) then x = X+hx=X+h, \Rightarrow⇒ x = X-1x=X−1

and y = Y+ky=Y+k \Rightarrow⇒ y = Y+2y=Y+2

From the given equation, the transformed equation is

(X-1)^{2}+(Y+2)^{2}+2(X-1)-4(Y+2)+1 = 0(X−1)

2

+(Y+2)

2

+2(X−1)−4(Y+2)+1=0

\Rightarrow⇒(X^{2}+1-2X)+(Y^{2}+4+4Y)+2X -2 -4Y-8+1=0(X

2

+1−2X)+(Y

2

+4+4Y)+2X−2−4Y−8+1=0

\Rightarrow⇒X^{2}+Y^{2}-4X

2

+Y

2

−4

This is the required transformed equation.