Question

16x2-y2 + 42. 16-0. Identify and sketch the surface EXAMPLE 7 Dividing by -16, we first put the equation into standard form: SOLUTION z2 16 4 Comparing this equation with equations of quadratic surfaces, we see that it represents a hyperboloid of two sheets the only difference being that in this case the axis of the hyperboloid is the y-axis The traces in the xy and yz-planes are the hyperbolas 16 and z2 =1 4 x=0. 16 The surface has no trace in the xz-plane, but traces in the vertical planes y = k for l kl > 4 are the ellipses z2 4 which can be written as x2 z2

Answer 1

2 2 t6 16 2 2 4- 16 2 2 2% 2 e trace in thh xz- blane, arc th ellip sa 2 2 2 Ek 16-1