By shifting the origin to the point $(- 1, 2)$ transform the equation $4 x^{2} + y^{2} + 8 x - 4 y + 4 = 0$ , axes remaining parallel.

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Solution

Origin being shifted to $(- 1, 2)$ , new equation is formed by replacing
$x \to x + 1, y \to y - 2$
$=> 4 (x + 1)^{2} + (y - 2)^{2} + 8 (x + 1) - 4 (y - 2) + 4 = 0 => 4 x^{2} + y^{2} + 16 x - 8 y + 28 = 0$

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