`f(x , y)=x^2+y^2+2a x+2b y+c=0` represents a circle. If `f(x ,0)=0` has equal roots, each being `2,` and `f(0,y)=0` has 2 and 3 as its roots, then the center of the circle is (a) `(2,5/2)` (b) Data is not sufficient (c) `(-2,-5/2)` (d) Data is inconsistent

Let f(x,y)=0 be the equation of a circle. If f(0,lamda)=0 has equal roots lamda=2,2 and f(lamda,0)=0 has roots lamda=(4)/(5),5 then the centre of the circle is

Suppose f(x,y)=0 is the equation of a circle such that f(x,1)=0 has equal roots (each equal to 2) and f(1,x)=0 also has equal roots (each equal to zero). The equation of circle is

f(x, y) = 0 is a circle such that f(0, lambda) = 0 and f(lambda, 0)=0 have equal roots and f(1, 1)= -2 then the radius of the circle is : (A) 4 (B) 8 (C) 2 (D) 1

The length of the tangent from (0, 0) to the circle 2(x^(2)+y^(2))+x-y+5=0 , is

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0

If the circle x^(2) +y^(2) + 2gx + 2fy + c = 0 bisects the circumference of the circle x^(2) +y^(2) + 2g'x + 2f'y + c' = 0 , them the length of the common chord of these two circles is

If the equation x^2+y^2+2h x y+2gx+2fy+c=0 represents a circle, then the condition for that circle to pass through three quadrants only but not passing through the origin is f^2> c (b) g^2>2 c >0 (d) h=0

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

Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5)=-3f(2) and that 3 is a root of f(x)=0. Then find the other of f(x)=0.