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Maths-

General

Easy

Question

The transformed equation of $x to the power of 2 end exponent minus y to the power of 2 end exponent plus 2 x plus 4 y equals 0$ when the origin is shifted to the point (-1,2) is

$X^{2} + 2 Y^{2} = 1$
$X^{2} + 3 Y^{2} = 1$
$X^{2} - Y^{2} + 3 = 0$
$4 X^{2} + 9 Y^{2} = 36$

The correct answer is: $X to the power of 2 end exponent minus Y to the power of 2 end exponent plus 3 equals 0$

Put x = X-1, y = Y+2
$left parenthesis x minus 1 right parenthesis to the power of 2 end exponent minus open parentheses y plus 2 close parentheses to the power of 2 end exponent plus 2 open parentheses x minus 1 close parentheses plus 4 open parentheses y plus 2 close parentheses equals 0$
$x to the power of 2 end exponent minus y to the power of 2 end exponent plus 3 equals 0$

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