1926　京都帝国大学　工学部第一次

【１】 From an elliptical plate with the major axis $2a=20\mathrm{cm}$ and the minor axis $2b=10\mathrm{cm}$ is required to get two discs of equal diameters.

 Calcurate the greatest possible diameter $2t$ of the discs.

【２】 A plane cuts a sphere of the radius $r=\mathrm{S}\mathrm{cm}$ into tow parts. What is the distance of the plane from the cntre of the sphere, if the ratio of the surface area should be $1:4\text{.}$

【３】 A cylindrical hole of the diameter $a$ is bored through the centre of a ball of radius $b\text{;}$ find the volume of the hole.

【４】 Any straight line $\mathrm{AB}$ drawn through a fixed point $\mathrm{A}$$(p,0)$ cuts the $y‐$axis at a point $\mathrm{B}\text{.}$

 Find the envelope of $\mathrm{BC}$ perpendicular to $\mathrm{AB}\text{.}$