If sum of the slopes of the lines given by $x^2-4 p x y+8 y^2=0$ is three times their product then $p=$ ...........

$$\frac{1-2\left[\cos 60^{\circ}-\cos 80^{\circ}\right]}{2 \sin 10^{\circ}}=\ldots \ldots$$

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is......

If $f(x)$ is continuous at $x=3$, where

$$\begin{aligned} f(x) & =a x+1, & \text { for } x \leq 3 \\ & =b x+3 & , \text { for } x>3 \text { then } \end{aligned}$$