Two lines are given by $x^2 - 4xy + 4y^2 + kx - 2ky = 0$, then the value of k so that the distance between them is 3 is

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

The tangent to the circle $x^2 + y^2 = 10$ at the point $(3,1)$ touches the circle $x^2 + y^2 - 2\sqrt{10}\,x - 20y + k = 0$, then the value of $k$ is...

If the eccentricity of the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1, (a > b)$ is $\dfrac{2}{3}$ and its focal chord is $3x + 2y - 6 = 0$, then the value of $a^2 + b^2$ is...