i) x2+y2+2x−y−z+3=0
then we group variables. We get equation. (x+1)2+(y−1/2)2+7/4=z
Finish formul is (x+1)2+(y−1/2)2=z−7/4
This formula is the formula of elliptic paraboloid (we then can see from standard form of elliptic paraboloid, z−z0=A(x−x0)2+B(y−y0)2 , where the coefficients A and B have the same sings )
Picture
ii) 3y2+3z2+4x+3y+z=9
Then, also we do group variables. We get the formula. 3(y+1/2)2−3/4+3(z+1/6)2−1/12=9−4x3(y+1/2)2+3(z+1/6)2=49/6−4x All numbers and variable x on the right side.
This is also elliptic paraboloid, but this elliptic paraboloid going on x-os.
Picture
Comments