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Obtaining Centre and Radius of a Circle from General Equation of a Circle

If x2+6+2i=y2...

Question

If $x^{2} + 6 + 2 i = (y^{2} - y) i + 5 x,$ then $(x, y)$ cannot be equal to

A

(2, 2)

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B

(- 1, 3)

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C

(3, 2)

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D

(2, - 1)

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Solution

The correct option is B $(- 1, 3)$
Given : $x^{2} + 6 + 2 i = (y^{2} - y) i + 5 x$
Comparing the real and imaginary part, we get
$x^{2} + 6 = 5 x$ and $y^{2} - y = 2$
$\Rightarrow x^{2} - 5 x + 6 = 0$ and $y^{2} - y - 2 = 0$
$\Rightarrow x = 2, 3$ and $y = 2, - 1$
Therefore, the correct ordered pairs of $(x, y)$ are $(2, 2), (2, - 1), (3, 2), (3, - 1)$

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Obtaining Centre and Radius of a Circle from General Equation of a Circle

Standard XII Mathematics

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