Coordinate Geometry: Straight Lines, Circles, Parabola, Ellipse and Hyperbola in Two Dimensions

In hyperbola, the length of the transverse axis is the distance between:

The center of the circle $4x^2 + 4y^2 - 8x + 12y - 25 = 0$ is:

The length of the latus rectum of $x^2 = -9y$ is equal to:

The eccentricity of the parabola is :

Let $x^2 = \frac{25}{2}y$ be the equation of a parabola, then the equation of its directrix is given by :

The equation of the conic section whose vertices are $(0, \pm 8)$ and asymptotes are $y = \pm \frac{4}{3}x$ is given by:

From point $Q$ which is outside the circle, the length of the tangent to the circle is $24\text{ cm}$ and the distance of $Q$ from the centre is $25\text{ cm}$, then the radius of the circle is given by :