(iv) 
The equation of the circle is
(Multiply by 2 we get)
![\[\begin{array}{*{35}{l}} {{x}^{2}}~+\text{ }{{y}^{2}}~+\text{ }2x\text{ }cos\text{ }\theta \text{ }+\text{ }2y\text{ }sin\text{ }\theta \text{ }-\text{ }8\text{ }=\text{ }0 \\ {{x}^{2}}~+\text{ }{{y}^{2}}~+\text{ }2ax\text{ }+\text{ }2by\text{ }+\text{ }c\text{ }=\text{ }0 \\ Centre\text{ }=\text{ }\left( -a,\text{ }-b \right) \\ =\text{ }\left[ \left( -2cos\text{ }\theta \right)/2\text{ },\text{ }\left( -2sin\text{ }\theta \right)/2 \right] \\ =\text{ }\left( -cos\text{ }\theta ,\text{ }-sin\text{ }\theta \right) \\ Radius\text{ }=~\surd \left( {{a}^{2}}~+\text{ }{{b}^{2}}~-\text{ }c \right) \\ =\text{ }\surd \left[ {{\left( -cos\text{ }\theta \right)}^{2}}~+\text{ }{{\left( sin\text{ }\theta \right)}^{2}}~\text{ }\left( -8 \right) \right] \\ =\text{ }\surd \left[ co{{s}^{2}}~\theta \text{ }+\text{ }si{{n}^{2}}~\theta \text{ }+\text{ }8 \right] \\ =\text{ }\surd \left[ 1\text{ }+\text{ }8 \right] \\ =\text{ }\surd \left[ 9 \right] \\ =\text{ }3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b7475b417cd6e3544eed2df59b5cee90_l3.png "Rendered by QuickLaTeX.com")
∴ The centre and radius of the circle is (-cos θ, -sin θ) and 3.
(iv) x2 + y2 – ax – by = 0
Equation of the circle is
![\[\begin{array}{*{35}{l}} {{x}^{2}}~+\text{ }{{y}^{2}}~-\text{ }ax\text{ }-\text{ }by\text{ }=\text{ }0 \\ ~{{x}^{2}}~+\text{ }{{y}^{2}}~+\text{ }2ax\text{ }+\text{ }2by\text{ }+\text{ }c\text{ }=\text{ }0 \\ Centre\text{ }=\text{ }\left( -a,\text{ }-b \right) \\ =\text{ }-\left( -\left( -a \right)/2,\text{ }-\left( -b \right)/2 \right) \\ =\text{ }\left( a/2,\text{ }b/2 \right) \\ Radius\text{ }=~\surd \left( {{a}^{2}}~+\text{ }{{b}^{2}}~-\text{ }c \right) \\ =\text{ }\surd \left[ {{\left( a/2 \right)}^{2}}~+\text{ }{{\left( b/2 \right)}^{2}} \right] \\ =~\surd \left[ \left( {{a}^{2}}/4\text{ }+\text{ }{{b}^{2}}/4 \right) \right] \\ =~\surd \left[ \left( {{a}^{2}}~+\text{ }{{b}^{2}} \right)/4 \right] \\ =\text{ }\left[ \surd \left( {{a}^{2}}~+\text{ }{{b}^{2}} \right) \right]/2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-97ce05367a04ebbfa0860cd3bd705fb7_l3.png "Rendered by QuickLaTeX.com")
∴ The centre and radius of the circle is (a/2, b/2) and [√(a2 + b2)]/2