The equation of a line passing through $(7, 4)$ and touching the circle $x^2 + y^2 - 6x + 4y - 3 = 0$ is:

The normal at a point $\theta$ to the curve $x=a(1+\cos \theta), y=a \sin \theta$ always passes through the fixed point

The area of the region (in sq. unit) bounded by the $x$-axis, the tangent, and the normal to the circle $x^2 + y^2 = 4$ drawn at the point $(1, \sqrt{3})$ is

The lines $y - y_1 = m(x - x_1) \pm a \sqrt{1 + m^2}$ are tangents to the same circle. The radius of the circle is:

$A$ line is a common tangent to the circle $(x-3)^{2}+y^{2}=9$ and the parabola $y^{2}=4x$. If the two points of contact $(a, b)$ and $(c, d)$ are distinct and lie in the first quadrant,then $2(a+c)$ is equal to ........ .

$A$ circle is such that $(x-2) \cos \theta + (y-2) \sin \theta = 1$ touches it for all values of $\theta$. Then,the circle is