A chord PQ of `(x^2)/(a^2)-(y^2)/(b^2)=1` touches the circle described on the line joining the foci as diameter. Then the tangents at P and Q meet on the curve:

Chords of the hyperbola x^2/a^2-y^2/b^2=1 are tangents to the circle drawn on the line joining the foci asdiameter. Find the locus of the point of intersection of tangents at the extremities of the chords.

Find the equation of the circle described on the line segment as diameter joining the foci of the parabolas x^2 =4ay and y^2 = 4a(x-a) as diameter.

AB and CD are two equal and parallel chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 . Tangents to the ellipse at A and B intersect at P and tangents at C and D at Q. The line PQ

Prove that the length of the intercept on the normal at the point P(a t^2,2a t) of the parabola y^2=4a x made by the circle described on the line joining the focus and P as diameter is asqrt(1+t^2) .

Prove that the length of the intercept on the normal at the point P(a t^2,2a t) of the parabola y^2=4a x made by the circle described on the line joining the focus and P as diameter is asqrt(1+t^2) .

If PQ is the focal chord of the parabola y^(2)=-x and P is (-4, 2) , then the ordinate of the point of intersection of the tangents at P and Q is

A line through the origin meets the circle x^(2)+y^(2)=a^(2) at P and the hyperbola x^(2)-y^(2)=a^(2) at Q. Prove that the locus of the point of intersection of tangent at P to the circle with the tangent at Q to the hyperbola is a straight line.

If any tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with centre C, meets its director circle in P and Q, show that CP and CQ are conjugate semi-diameters of the hyperbola.

The straight line x-2y+1=0 intersects the circle x^(2)+y^(2)=25 in points P and Q the coordinates of the point of intersection of tangents drawn at P and Q to the circle is

The straight line x-2y+5=0 intersects the circle x^(2)+y^(2)=25 in points P and Q, the coordinates of the point of the intersection of tangents drawn at P and Q to the circle is