Question

when the axes are translated to the point (-1,1) then the transformed equation of the curve x square +2 y square +2 x - 4y +2 = 0 is...

Answer 1

Step-by-step explanation:

let x + 1 = X

and y-2 = Y

therefore x = X - 1

and y = Y + 2

2y^2 +2x - 4y +2 = 0

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

2(Y^2 + 4Y + 4) + 2X - 2 -4Y -8 +2 = 0

2Y^2 + 8Y + 8 + 2X - 2 -4Y -8 +2 = 0

2Y^2 + 4Y + 2X = 0

Answer 2

Concept

Translated points

When the origin is moved to (X,Y), the point (x,y) on the line changes to (X,Y) (h,k)

Then, x=X+h,y=Y+k

Given

The equation of is curve x²+2y²+2x-4y+2=0.

To find

We have to find the equation of is curve when the axes are translated to the point (-1,1).

Solution

Since then, the axes have been translated. As a result, x and y become x = X - 1 and y = Y + 2 respectively.

Now, replace these values in the equation curve.

(X-1)²+2(Y + 2)² + 2(X-1) -4(Y + 2) + 2 = 0

(X-1)²+(Y² + 4Y + 4) + 2X - 2 -4Y -8 +2 = 0

(X-1)²+2Y² + 8Y + 8 + 2X - 2 -4Y -8 +2 = 0

X²+1-2X+2Y² + 4Y + 2X = 0

X²+2Y²+4Y+1 = 0

As a result, when the axes are translated, the equation of curve is X2+2Y2+4Y+1 = 0.