The complex number with argument $$\frac{5 \pi^{\mathrm{c}}}{6}$$ at a distance of 2 units from the origin is

If $$\bar{a}=3 \hat{i}-5 \hat{j}, \bar{b}=6 \hat{i}+3 \hat{j}$$ are two vectors and $$\bar{c}$$ is a vector such that $$\bar{c}=\bar{a} \times \bar{b}$$, then $$a: b$$ : is

If the polar co-ordinates of a point are $$\left(\sqrt{2}, \frac{\pi}{4}\right)$$, then its Cartesian co-ordinates are

The equation of the circle whose centre lies on the line $$x-4 y=1$$ and which passes through the points $$(3,7)$$ and $$(5,5)$$ is