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

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 (A) sqrt3 (B) 2 (C) 2sqrt2 (D) sqrt5

The vertices of the hyperbola 9x^2 - 16y^2 = 144

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is

A tangent to the hyperbola y = (x+9)/(x+5) passing through the origin is

Find the vertices, foci for the hyperbola 9x^(2)-16y^(2)=144 .

If the foci of (x^2)/(a^2)-(y^2)/(b^2)=1 coincide with the foci of (x^2)/(25)+(y^2)/9=1 and the eccentricity of the hyperbola is 2, then a^2+b^2=16 there is no director circle to the hyperbola the center of the director circle is (0, 0). the length of latus rectum of the hyperbola is 12

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__________

Find the vertices, foci for the hyperbola 9x^(2)-16y^(2)=144.