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 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

If the tangent at the point p on the circle x^(2)+y^(2) +6x +6y-2=0 meets the straight line 5x-2y+ 6 =0 at the point Q on the y-axis, then the length of PQ is-

The angle between the two tangents drawn from a point p to the circle x^(2)+y^(2)=a^(2) is 120^(@) . Show that the locus of P is the circle x^(2)+y^(2)=(4a^(2))/(3)

If the tangent at the point P on the circle x^2+y^2+6x+6y=2 meets the straight line 5x - 2y + 6 = 0 at a point on the y-axis, then the length of PQ is

If sec alpha and "cosec" alpha are the roots of x^(2)- px+q=0 then show that p^(2)=q(q+2)

The chord of contact of tangents drawn from a point on the circle x^2 + y^2 = a^2 to the circle x^2 + y^2 = b^2 touches the circle x^2 + y^2=c^2 Show that a, b, c are in G.P.

Let P be a point on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and the line through P parallel to the y-axis meets the circle x^(2)+y^(2)=9 at Q, where P,Q are on the same side of the x-axis. If R is a point on PQ such that (PR)/(RQ)=(1)/(2) , then the locus of R is

In the equation x^2-px+q=0 one root is twice of other then prove that 2p^2=9q

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 cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)