Find the value of a if
`2x^(2)+ay^(2)-2x+2y-1=0` represents a circle and also find its radius.
(ii) Find the values of a,b if
`ax^(2)+bxy+3y^(2)-5x+2y-3=0` represents a circle. Also find the radius and centre of the circle.
(iii) If `x^(2)+y^(2)+2gx+2fy=0` represents a circle with centre (-4,-3) then find g,f and the radius of the circle.
(iv) If the circle `x^(2)+y^(2)+ax+by-12=0` has the centre at (2,3) then find a ,b and the raidus of the circle.
(v) If the circle `x^(2)+y^(2)-5x+6y-a=0` has radius 4 , find a

Answer

(i) `a=2` radius `=(sqrt(21))/4`
(ii) a=3, b=0 radius `=(sqrt(65))/6`, centre `=(5/6,(-1)/3)`
(iii) g=4,f=3 , radius =5
(iv) `a=-4, b=-6, 4=6` (v) a=-3