Questions in circle

Select	Question
	The equation of the circle through the points of intersection of ${{x}^{2}}+{{y}^{2}}-1=0$ , ${{x}^{2}}+{{y}^{2}}-2x-4y+1=0$ and touching the line $x+2y=0$ , is
	If the circles ${{x}^{2}}+{{y}^{2}}-9=0$ and ${{x}^{2}}+{{y}^{2}}+2ax+2y+1=0$ touch each other, then $a =$
	The equation of the circle which passes through the origin, has its centre on the line $x+y=4$ and cuts the circle ${{x}^{2}}+{{y}^{2}}-4x+2y+4=0$ orthogonally, is
	Two given circles ${{x}^{2}}+{{y}^{2}}+ax+by+c=0$ and ${{x}^{2}}+{{y}^{2}}+dx+ey+f=0$ will intersect each other orthogonally, only when
	The condition of the curves $a{{x}^{2}}+b{{y}^{2}}=1$ and $a'{{x}^{2}}+b'{{y}^{2}}=1$ to intersect each other orthogonally, is
	The radical centre of the circles ${{x}^{2}}+{{y}^{2}}+4x+6y=19,{{x}^{2}}+{{y}^{2}}=9$ and ${{x}^{2}}+{{y}^{2}}-2x-2y=5$ will be
	The locus of the centres of the circles which touch externally the circles ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$ and ${{x}^{2}}+{{y}^{2}}=4ax$ , will be
	If the circles of same radius a and centers at (2, 3) and (5, 6) cut orthogonally, then $a =$
	The equation of a circle passing through origin and co-axial to circles ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$ and ${{x}^{2}}+{{y}^{2}}+2ax=2{{a}^{2}},$ is
	The equation of the circle which passes through the point of intersection of circles ${{x}^{2}}+{{y}^{2}}-8x-2y+7=0$ and ${{x}^{2}}+{{y}^{2}}-4x+10y+8=0$ and having its centre on$y$ -axis, will be