If `P and Q` a be a pair of conjugate points with respect to a circle `S`. Prove that the circle on `PQ` as diameter cuts the circle `S` orthogonally.

If the chord of contact of tangents from a point P to a given circle passes through Q , then the circle on P Q as diameter. cuts the given circle orthogonally touches the given circle externally touches the given circle internally none of these

Prove that the diameter is the greatest chord in a circle.

Prove that the diameter is the greatest chord in a circle.

The tangent at a point P on an ellipse intersects the major axis at T ,a n dN is the foot of the perpendicular from P to the same axis. Show that the circle drawn on N T as diameter intersects the auxiliary circle orthogonally.

The tangent at a point P on an ellipse intersects the major axis at T ,a n dN is the foot of the perpendicular from P to the same axis. Show that the circle drawn on N T as diameter intersects the auxiliary circle orthogonally.

Find the equation of the circle when the end points of a diameter of the circle are : (p, q) and (r, s)

The normal at the point (3, 4) on a circle cuts the circle at the point (-1,-2). Then the equation of the circle is

If a diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel.

If a diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel.

If the chord of contact of a point A with respect to the circle x^(2)+y^(2)=a^(2) cut the circle at P and Q such that |___(POQ)=90^(@) then show that locus of A is x^(2)+y^(2)=2a^(2) .