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

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

A circle is drawn whose centre is on the x - axis and it touches the y - axis. If no part of the circle lies outside the parabola y^(2)=8x , then the maximum possible radius of the circle is

From the focus of the parabola y^2=2px as centre, a circle is drawn so that a common chord of the curve is equidistant from the vertex and the focus. The radius of the circle is

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

Write the eccentricity of the hyperbola 9x^2-16 y^2=144.

In the hyperbola 16 x^(2) - 9y^(2) =144 , the value of eccentricity is

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. Equation of ellipse is : (A) x^2/16 + y^2/9 =1 (B) x^2/25 + y^2/9 = 1 (C) x^2/25 + y^2/16 = 1 (D) none of these

The eccentricity of the hyperbola 9x^(2) -16y^(2) =144 is

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