If the axes are transformed to the point (-1, | vedclass

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(B) When the origin is shifted to the point $(h, k) = (-1, 1)$,the new coordinates $(X, Y)$ are related to the old coordinates $(x, y)$ by the equatio

Vedclass · Accepted Answer

$3x^2 + y^2 - 4x + 6y + 21 = 0$

Vedclass · Answer

(B) When the origin is shifted to the point $(h, k) = (-1, 1)$,the new coordinates $(X, Y)$ are related to the old coordinates $(x, y)$ by the equations: $x = X + h = X - 1$ $y = Y + k = Y + 1$ Substituting these into the given equation $3x^2 + y^2 + 2x + 4y + 15 = 0$: $3(X - 1)^2 + (Y + 1)^2 + 2(X - 1) + 4(Y + 1) + 15 = 0$ $3(X^2 - 2X + 1) + (Y^2 + 2Y + 1) + 2X - 2 + 4Y + 4 + 15 = 0$ $3X^2 - 6X + 3 + Y^2 + 2Y + 1 + 2X - 2 + 4Y + 4 + 15 = 0$ $3X^2 + Y^2 - 4X + 6Y + 21 = 0$ Thus,the transformed equation is $3x^2 + y^2 - 4x + 6y + 21 = 0$.

If the axes are transformed to the point $(-1, 1)$,then the equation $3x^2 + y^2 + 2x + 4y + 15 = 0$ would transform to:

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