If `O` is the origin and `O Pa n dO Q` are the tangents from the origin to the circle `x^2+y^2-6x+4y+8-0` , then the circumcenter of triangle `O P Q` is `(3,-2)` (b) `(3/2,-1)` `(3/4,-1/2)` (d) `(-3/2,1)`

Find the equations of the tangents drawn from the point A(3, 2) to the circle x^2 + y^2 + 4x + 6y + 8 = 0

The length of the tangent of the circle x^2+y^2-2x-y -7 = 0 from the point (-1,-3) is

Find the area of the equilateral triangle inscribed in the circle x^(2) + y^(2) - 4x + 6y - 3 = 0 .

Find the equations of the tangents drawn to the curve y^2-2x^3-4y+8=0 from the point (1,\ 2) .

The centre of the circle lambdax^2+(2lambda-3)y^2-4x+6y-1=0 is

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). (a) x y=4 (b) x y=1/4 x y=1 (d) none of these

The number of common tangents that can be drawn to the circles x^2+y^2-4x-6y-3=0 and x^2+y^2+2x+2y+1=0 is :

a variable plane which is at a constant distance 3p from the origin O cuts the axes at A,B,C. Show that the locus of the centroid of the triangle ABC is x^(-2)+y^(-2)+z^(-2)=p^(-2) .

Equation of a circle having radius equal to twice the radius of the circle x^2+y^2+(2p +3)x + (3-2p)y +p-3 = 0 and touching it at the origin is

The equations of tangents to the circle x^2+y^2-6x-6y+9=0 drawn from the origin in (a). x=0 (b) x=y (c) y=0 (d) x+y=0