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If the axes are shifted to the point {({1},-{2})} without rota

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If the axes are shifted to the point $(1, - 2)$ without rotation, what do the following equations become? $2 x^{2} + y^{2} - 4 x + 4 y = 0$ $y^{2} - 4 x + 4 y + 8 = 0$

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If the axes are shifted to the point

(1, - 2)

without rotation, what do the following equations become?

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

y^{2} - 4 x + 4 y + 8 = 0

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Text solutionVerified

Solution: First equation

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

2 (x - 1)^{2} + (y + 2)^{2} - 4 (x - 1) + 4 (y + 2) = 0

2 (x^{2} + 1 - 2 x) + y^{2} + 4 + 4 y - 4 x + 4 + 4 y + 8 = 0

2 x^{2} + 2 - 2 x + y^{2} + 4 - 4 y - 4 x + 4 + 4 y + 8 = 0

2 x^{2} + y^{2} - 6 x + 8 y + 18 = 0

y^{2} - 4 x + 4 y + 8 = 0

y^{2} + 8 y - 4 x + 24 = 0

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Question Text	If the axes are shifted to the point $(1, - 2)$ without rotation, what do the following equations become? $2 x^{2} + y^{2} - 4 x + 4 y = 0$ $y^{2} - 4 x + 4 y + 8 = 0$
Answer Type	Text solution:1
Upvotes	150