The parametric equations of the curve x^2+y^2 | vedclass

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(D) The given equation is $x^2+y^2-ax-by=0$. Completing the square,we get: $(x-\frac{a}{2})^2 + (y-\frac{b}{2})^2 = \frac{a^2+b^2}{4}$. This represent

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$x=\frac{a}{2}+\sqrt{\frac{a^2+b^2}{4}} \cos 	heta, y=\frac{b}{2}+\sqrt{\frac{a^2+b^2}{4}} \sin 	heta$

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(D) The given equation is $x^2+y^2-ax-by=0$. Completing the square,we get: $(x-\frac{a}{2})^2 + (y-\frac{b}{2})^2 = \frac{a^2+b^2}{4}$. This represents a circle with center $(h, k) = (\frac{a}{2}, \frac{b}{2})$ and radius $r = \sqrt{\frac{a^2+b^2}{4}}$. The parametric equations of a circle are $x = h + r \cos 	heta$ and $y = k + r \sin 	heta$. Substituting the values,we get $x = \frac{a}{2} + \sqrt{\frac{a^2+b^2}{4}} \cos 	heta$ and $y = \frac{b}{2} + \sqrt{\frac{a^2+b^2}{4}} \sin 	heta$.

The parametric equations of the curve $x^2+y^2-ax-by=0$ are

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