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)` (c)`(3/4,-1/2)` (d) `(-3/2,1)`

If O Aa n dO B are equal perpendicular chords of the circles x^2+y^2-2x+4y=0 , then the equations of O Aa n dO B are, where O is the origin.

Find the centre and radius of the circle 3x^(2)+(a+1)y^(2)+6x-9y+a+4=0 .

If O is the origin, O P=3 with direction ratios -1,2,a n d-2, then find the coordinates of Pdot

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 (c) x y=1 (d) none of these

Find the equation of tangents to circle x^(2)+y^(2)-2x+4y-4=0 drawn from point P(2,3).

Find 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

If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at Aa n dB , then the locus of the centroud of triangle O A B is (a) x^2+y^2=(2k)^2 (b) x^2+y^2=(3k)^2 (c) x^2+y^2=(4k)^2 (d) x^2+y^2=(6k)^2

A line meets the coordinate axes at A and B . A circle is circumscribed about the triangle O A Bdot If d_1a n dd_2 are distances of the tangents to the circle at the origin O from the points Aa n dB , respectively, then the diameter of the circle is (2d_1+d_2)/2 (b) (d_1+2d_2)/2 d_1+d_2 (d) (d_1d_2)/(d_1+d_2)

The locus of the midpoints of the chords of contact of x^2+y^2=2 from the points on the line 3x+4y=10 is a circle with center Pdot If O is the origin, then O P is equal to 2 (b) 3 (c) 1/2 (d) 1/3