The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are $(1,2)$ and $(4,5)$ is

The coordinate axes are rotated about the origin in the counter clockwise direction through an angle $60^{\circ}$. If a and $b$ are the intercepts made on the new axes by a straight line whose equation referred to the original axes is $x+y=1$, then $\frac{1}{a^2}+\frac{1}{b^2}=$

The image of a point $(2,-1)$ with respect to the line $x-y+1=0$ is

If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction, then the equation of that line is