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Expansions to Remove Indeterminate Form

The parametri...

Question

The parametric coordinates of any point on the circle $x^{2} + y^{2} - 4 x - 4 y = 0$ are-

(- 2 + 2 cos α, - 2 + 2 sin α)

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(2 + 2 cos α, 2 + 2 sin α)

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(2 + 2 \sqrt{2} cos α, 2 + 2 \sqrt{2} sin α)

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(- 2 + 2 \sqrt{2} cos α, - 2 + 2 \sqrt{2} sin α)

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Solution

The correct option is C $(2 + 2 \sqrt{2} cos α, 2 + 2 \sqrt{2} sin α)$
$x^{2} + y^{2} - 4 x - 4 y = 0$
$\Rightarrow (x - 2)^{2} + (y - 2)^{2} = (2 \sqrt{2})^{2}$
Hence any parametric point on the circle is given by,
$(2 + 2 \sqrt{2} cos α, 2 + 2 \sqrt{2} sin α)$

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