If a variable point $(x, y)$ satisfies the equation $x^2 + y^2 - 8x - 6y + 9 = 0$,then the range of $\frac{y}{x}$ is

If two circles of the same radius $a$ and centers at $(2, 3)$ and $(5, 6)$ are orthogonal,find the value of $a$.

$A$ common tangent to $9x^2 + 16y^2 = 144$,$y^2 - x + 4 = 0$,and $x^2 + y^2 - 12x + 32 = 0$ is:

Let $y^2 = 4ax$ be a parabola and $x^2 + y^2 + 2bx = 0$ be a circle. If the parabola and the circle touch each other externally,then:

The number of real circles cutting orthogonally the circle $x^{2}+y^{2}+2x-2y+7=0$ is

Let the tangent and normal at the point $(3 \sqrt{3}, 1)$ on the ellipse $\frac{x^2}{36} + \frac{y^2}{4} = 1$ meet the $y$-axis at the points $A$ and $B$ respectively. Let the circle $C$ be drawn taking $AB$ as a diameter and the line $x = 2 \sqrt{5}$ intersect $C$ at the points $P$ and $Q$. If the tangents at the points $P$ and $Q$ on the circle intersect at the point $(\alpha, \beta)$,then $\alpha^2 - \beta^2$ is equal to