Let the slope of a diameter $AC$ of a circle of radius $25$ units be $\frac{3}{4}$. If $(3, 2)$ is the centre of the circle,$A = (x_1, y_1)$ and $C = (x_2, y_2)$,then $\frac{x_1 x_2}{y_1 y_2} = $

For each natural number $k$,let $C_k$ denote the circle with radius $k$ centimeters and center at the origin. On the circle $C_k$,a particle moves $k$ centimeters in the counter-clockwise direction. After completing its motion on $C_k$,the particle moves to $C_{k+1}$ in the radial direction. The motion of the particle continues in this manner. The particle starts at $(1, 0)$. If the particle crosses the positive direction of the $x$-axis for the first time on the circle $C_n$,then $n$ is equal to

$A$ point inside the circle $x^2 + y^2 + 3x - 3y + 2 = 0$ is

Suppose $d_1$ and $d_2$ are respectively the lengths of intercepts of the circles $x^2+y^2=4$ and $x^2+y^2-10x-14y+65=0$ on the line $2x-2y-3=0$. Then,which of the following is true?

Two tangents are drawn from the point $P(-1, 1)$ to the circle $x^{2}+y^{2}-2x-6y+6=0$. If these tangents touch the circle at points $A$ and $B$,and if $D$ is a point on the circle such that the lengths of the segments $AB$ and $AD$ are equal,then the area of the triangle $ABD$ is equal to:

The angle subtended at the centre of a circle of radius $3 \text{ metres}$ by an arc of length $1 \text{ metre}$ is equal to