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Implicit Differentiation

Find the orde...

Question

Find the ordered pair (x, y) for which $x^{2} - y^{2} - i (2 x + y) = 2 i$

x = - 2

and

y = 2

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x = 2

and

y = - 2

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x = \frac{- 2}{3}

and

y = \frac{2}{3}

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x = \frac{2}{3}

and

y = - \frac{2}{3}

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Solution

The correct option is A $x = - 2$ and $y = 2$
We have
$x^{2} - y^{2} = 0$ or $x = \pm y$
and $- (2 x + y) = 2$ (1)
or $2 x + y = - 2$ (2)
Solving $x = y$ with (2), we have $x = y = - \frac{2}{3}$
Solving $x = - y$ with (2), we have $x = - 2$ and $y = 2$
Ans: A

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