If variable point $(x, y)$ satisfies the equation $x^2 + y^2 -8x -6y + 9 = 0$ , then range of $\frac{y}{x}$ is
$\left[ { - \frac{7}{{24}},\frac{7}{{24}}} \right]$
$\left[ { - \frac{7}{{24}},\infty } \right)$
$\left[ {\frac{7}{{24}},\infty } \right)$
$\left( { - \infty ,\infty } \right)$
If the straight line $ax + by = 2;a,b \ne 0$ touches the circle ${x^2} + {y^2} - 2x = 3$ and is normal to the circle ${x^2} + {y^2} - 4y = 6$, then the values of a and b are respectively
The equations of the tangents to the circle ${x^2} + {y^2} - 6x + 4y = 12$ which are parallel to the straight line $4x + 3y + 5 = 0$, are
The equations of the tangents to circle $5{x^2} + 5{y^2} = 1$, parallel to line $3x + 4y = 1$ are
A tangent drawn from the point $(4, 0)$ to the circle $x^2 + y^2 = 8$ touches it at a point $A$ in the first quadrant. The co-ordinates of another point $B$ on the circle such that $l\, (AB) = 4$ are :
If the line $y = \sqrt 3 x + k$ touches the circle ${x^2} + {y^2} = 16$, then $k =$