Let the centre of the circle $x^2+y^2+2 \mathrm{~g} x+2 f y+25=0$ be in the first quadrant and lie on the line $2 x-y=4$. Let the area of an equilateral triangle inscribed in the circle be $27 \sqrt{3}$. Then the square of the length of the chord of the circle on the line $x=1$ is $\_\_\_\_$ .

Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line $x + y = 1$ is $\sqrt{14}$, then the square of the radius of C is ________.

Let $C$ be the circle $x^2+(y-1)^2=2, E_1$ and $E_2$ be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line $x+y=3$ touch the curves $C, E_1$ and $E_2$ at $P\left(x_1, y_1\right), Q\left(x_2, y_2\right)$ and $R\left(x_3, y_3\right)$ respectively. Given that $P$ is the mid point of the line segment $Q R$ and $P Q=\frac{2 \sqrt{2}}{3}$, the value of $9\left(x_1 y_1+x_2 y_2+x_3 y_3\right)$ is equal to _______.