With one focus of the hyperbola `x^2/9-y^2/16=1` as the centre, a circle is drawn which is tangent to the hyperbola with no part of the circle being outside the hyperbola. The radius of the circle is

The foci of the hyperbola 4x^2-9y^2=36 is

An ellipse is drawn with major and minor axis of length 10 and 8 respectively. Using one focus a centre, a circle is drawn that is tangent to ellipse, with no part of the circle being outside the ellipse. The radius of the circle is

The centre of the hyperbola 9x^2-16y^2-18x+64y-199=0 is

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

PQ is the double ordinate of the hyperbola x^2/a^2-y^2/b^2=1 and O is the centre of the hyperbola. If triangle OPQ is an equilateral triangle, then show that the eccentricity of this hyperbola is e) e^2 >4/3

The eccentricity of the hyperbola 4x^(2)-9y^(2) =36 is:

The locus of the centre of a circle radius 2 which rolls on the outside of the circle x^2+y^2+3x-6y-9=0 is

A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), subtends a right angle at the center of the hyperbola if this chord touches. a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0, 0).

Let 'p' be the perpendicular distance from the centre C of the hyperbola x^2/a^2-y^2/b^2=1 to the tangent drawn at a point R on the hyperbola. If S & S' are the two foci of the hyperbola, then show that (RS + RS')^2 = 4 a^2(1+b^2/p^2) .

If the chord xcosalpha+ysinalpha=p of the hyperbola (x^2)/(16)-(y^2)/(18)=1 subtends a right angle at the center, and the diameter of the circle, concentric with the hyperbola, to which the given chord is a tangent is d , then the value of d/4 is__________