State the type of the quadratic surface: x2+(y6)2+z2=1 1. hyperboloid of two sheets 2. hyperboloid of one sheet 3. ellipsoid 4. none of these

solution:

quadratic surface,

x^{2}+z^{2}+\frac{y^{2}}{36}=1

=x^{2}+z^{2}=1-\frac{y^{2}}{36}

=\frac{x^{2}}{a^{2}}+\frac{z^{2}}{c^{2}}=1-\frac{y^{2}}{b^{2}}

this is a hyperbolid of one that intersection at  

y=0

the quadratic surface becomes

x^{2}+z^{2}=1

this is the equation of the unit circle

so,the surface is three circle