If two distinct chords, drawn from the point (p, q) on the circle `x^2+y^2=p x+q y` (where `p q!=q)` are bisected by the x-axis, then (a) `p^2=q^2` (b) `p^2=8q^2` `p^2<8q^2` (d) `p^2>8q^2`

If two distinct chords, drawn from the point (p,q) on the circle x^(2)+y^(2)=px+qy (where pq ne 0) are bisected by the x-axis then show that, p^(2) gt 8 q^(2)

If the roots of the equation x^2+2px+q=0 and x^2+2qx+p=0 where p!=q .Differ by a constant ,prove that p+q+1=0

If p and q are the roots of the equation x^2+px+q =0, then

If p,q are odd integers, then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, then find the value of p and q , where p and q are real.

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=0

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tangents are drawn from any point on this tangant to the circle x^2+y^2=a^2 , such that the chords of contact pass through a fixed point (r , s) . Then p ,q ,r and s can hold the relation (a) r^2q=4p^2s (b) r q^2=4p s^2 (c) r q^2=-4p s^2 (d) r^2q=-4p^2s

The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with abscissa 1. Then the value of pa n dq for which the distance between the vertex of the parabola and the x-axis is the minimum is (a) p=-1,q=-1 (b) p=-2,q=0 (c) p=0,q=-2 (d) p=3/2,q=-1/2

IF 2+sqrt3i is a root of the equation x^2+px+q=0 where p and q are real, find p and q.