For the circle `ax^(2)+y^(2)+bx+dy+2=0` centre is `(1,2)` then `2b+3d`=

A straight line is drawn through the centre of the circle x^(2)+y^(2)-2ax=0 line x+2y=0 parallel to the straight and intersecting the circle at A and B. Then the area of triangle AOB is

If a tangent having slope 2 of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is normal to the circle x^(2)+y^(2)+bx+1=0 , then the vlaue of 4a^(2)+b^(2) is equal to

A straight line is drawn through the centre of the circle x^(2)+y^(2)-1ax=0 parallel to the straight line x+2y=0 and intersection the circle at A and B. Then the area of AOB is

Coordinates of the centre of the circle which bisects the circumferences of the circles x^(2)+y^(2)=1;x^(2)+y^(2)+2x-3=0 and x^(2)+y^(2)+2y-3=0 is

If two distinct chords drawn from the point (a, b) on the circle x^2+y^2-ax-by=0 (where ab!=0) are bisected by the x-axis, then the roots of the quadratic equation bx^2 - ax + 2b = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

The radical centre of the circles x^(2)+y^(2)=9 , x^(2)+y^(2)-2x-2y-5=0 , x^(2)+y^(2)+4x+6y-19=0 is A) (0,0) (B) (1,1) (C) (2,2) (D) (3,3)

If the expression ax^(3) + 2x^(2) y - bx y^(2) -2y^(3) is symmetric, then (a,b) =

Equation of the circle with centre at (1,-2) , and passing through the centre of the circle x^(2) + y^(2) + 2y - 3 = 0 , is

Let the coefficients in the cubic equation ax^(3)+bx^(2)+cx+d=0 be related by -a+b-c+d=3 and 8x+4b+2c+d=6 Show that the quadratic equation 3ax^(2)+2bx+c-1 has a root in (-1,2)