Suppose a circle passes through $(2,2)$ and $(9,9)$ and touches the $X$-axis at $P$. If $O$ is the origin,then $OP$ is equal to

If $(m_i, \frac{1}{m_i}), i = 1, 2, 3, 4$ are concyclic points,then the value of $m_1 \cdot m_2 \cdot m_3 \cdot m_4$ is

Let $S$ be the set of all points $\left(\frac{a}{b}, \frac{c}{d}\right)$ on the circle with radius $1$ centered at $(0,0)$,where $a$ and $b$ are relatively prime integers,$c$ and $d$ are relatively prime integers (that is,$\operatorname{HCF}(a, b) = \operatorname{HCF}(c, d) = 1$),and the integers $b$ and $d$ are even. Then,the set $S$ is:

Let $l > 0$ be a real number,$C$ denote a circle with circumference $l$,and $T$ denote a triangle with perimeter $l$. Then:

$A$ line $l$ meets the circle $x^2+y^2=61$ at points $A$ and $B$. Given that $P(-5, 6)$ is a point such that $PA=PB=10$,find the equation of line $l$.

The minimum distance and maximum distance of the point $P(2,-7)$ from the circle $x^2+y^2-14x-10y-151=0$ are respectively . . . . . . units.