When the coordinate axes are rotated about the origin in the positive direction through an angle $\frac{\pi}{4}$, if the equation $49 x^2+25 y^2=1225$ is transformed to $p x^2+q x y+r y^2=t$ and the GCD of $p, q, r, t$ is 1 , then

If the eccentricity and the length of the latusrectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ are $\frac{\sqrt{3}}{2}$ and 1 respectively, then the sum of the lengths of major axis and minor axis of the ellipse is

The parametric equations of the ellipse whose focii are $(-3,0),(9,0)$ and eccentricity is $\frac{1}{3}$, are

If $a \alpha^2+b \beta^2+c \alpha \beta+d=0$ is the transformed equation of $4 x^2+\sqrt{3} x y+5 y^2-4=0$ obtained by using $\alpha=\frac{\sqrt{3}}{2} x+\frac{y}{2}$ and $\beta=-\frac{x}{2}+\frac{\sqrt{3}}{2} y$, then $c(a+b+d)=$