The transformed equation of the curve 2x^2+y^ | vedclass

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Question

(A) Given that the origin is translated from $(0, 0)$ to $(h, k) = (-1, 2)$.We use the transformation equations $x = X + h$ and $y = Y + k$.Substituti

Vedclass · Accepted Answer

$2x^2+y^2-7x+9y+11=0$

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(A) Given that the origin is translated from $(0, 0)$ to $(h, k) = (-1, 2)$.We use the transformation equations $x = X + h$ and $y = Y + k$.Substituting the values,we get $x = X - 1$ and $y = Y + 2$.Substitute these into the original equation $2x^2 + y^2 - 3x + 5y - 8 = 0$:$2(X - 1)^2 + (Y + 2)^2 - 3(X - 1) + 5(Y + 2) - 8 = 0$$2(X^2 - 2X + 1) + (Y^2 + 4Y + 4) - 3X + 3 + 5Y + 10 - 8 = 0$$2X^2 - 4X + 2 + Y^2 + 4Y + 4 - 3X + 5Y + 5 = 0$Combining like terms: $2X^2 + Y^2 - 7X + 9Y + 11 = 0$.Replacing $(X, Y)$ with $(x, y)$,the transformed equation is $2x^2 + y^2 - 7x + 9y + 11 = 0$.

The transformed equation of the curve $2x^2+y^2-3x+5y-8=0$ when the origin is translated to the point $(-1, 2)$ is

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