The point to which the origin is to be shifte | vedclass

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(A) Given equation is $4x^2 + 9y^2 - 8x + 36y + 4 = 0$. To eliminate the $x$ and $y$ terms,we shift the origin to $(h, k)$. Let $x = X + h$ and $y = Y

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$(1, -2)$

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(A) Given equation is $4x^2 + 9y^2 - 8x + 36y + 4 = 0$. To eliminate the $x$ and $y$ terms,we shift the origin to $(h, k)$. Let $x = X + h$ and $y = Y + k$. Substituting these into the equation: $4(X+h)^2 + 9(Y+k)^2 - 8(X+h) + 36(Y+k) + 4 = 0$. Expanding the terms: $4(X^2 + 2hX + h^2) + 9(Y^2 + 2kY + k^2) - 8X - 8h + 36Y + 36k + 4 = 0$. Grouping the linear terms: $(8h - 8)X + (18k + 36)Y + (4h^2 + 9k^2 - 8h + 36k + 4) = 0$. For the $X$ and $Y$ terms to be eliminated,their coefficients must be zero: $8h - 8 = 0 \implies h = 1$. $18k + 36 = 0 \implies k = -2$. Thus,the origin is shifted to $(1, -2)$.

The point to which the origin is to be shifted to eliminate $x$ and $y$ terms of the equation $4x^2+9y^2-8x+36y+4=0$ is

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