Questions in circle

Select	Question
	The equation of line passing through the points of intersection of the circles $3{{x}^{2}}+3{{y}^{2}}-2x+12y-9=0$ and ${{x}^{2}}+{{y}^{2}}+6x+2y-15=0$ , is
	From any point on the circle ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$ tangents are drawn to the circle ${{x}^{2}}+{{y}^{2}}={{a}^{2}}{{\sin }^{2}}\alpha $ , the angle between them is
	The equation of the circle through the point of intersection of the circles ${{x}^{2}}+{{y}^{2}}-8x-2y+7=0$ , ${{x}^{2}}+{{y}^{2}}-4x+10y+8=0$ and (3, –3) is
	The equation of circle which passes through the point (1,1) and intersect the given circles ${{x}^{2}}+{{y}^{2}}+2x+4y+6=0$ and ${{x}^{2}}+{{y}^{2}}+4x+6y+2=0$ orthogonally, is
	Two circles ${{S}_{1}}={{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0$ and ${{S}_{2}}={{x}^{2}}+{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0$ cut each other orthogonally, then
	Circles ${{x}^{2}}+{{y}^{2}}+2gx+2fy=0$ and ${{x}^{2}}+{{y}^{2}}$ $+2g'x+2f'y=$ $0$ touch externally, if
	The two circles ${{x}^{2}}+{{y}^{2}}-2x-3=0$ and ${{x}^{2}}+{{y}^{2}}-4x-6y-8=0$ are such that
	One of the limit point of the coaxial system of circles containing ${{x}^{2}}+{{y}^{2}}-6x-6y+4=0$ , ${{x}^{2}}+{{y}^{2}}-2x$ $-4y+3=0$ is
	The equation of the circle having the lines ${{x}^{2}}+2xy+3x+6y=0$ as its normals and having size just sufficient to contain the circle $x(x-4)+y(y-3)=0$ is
	Locus of the point, the difference of the squares of lengths of tangents drawn from which to two given circles is constant, is