Name the type of equation surface 4x2 ay2 49Z2 0 x2 4y2

Name the type of equation surface 4x2 + ay2 - 49Z2 = 0 x2 + 4y2 + Z2 - ZX = 0 Hint: Completed the Square on X

Solution

a)

4x^2 + 9y^2 = 49z^2

Therefore

z^2 = x^2/(49/4) + y^2/(49/9)

It has resemblence with Ellipse and the Cone Equations

So It is the Equation of Cone with Elliptical Base

which is Elliptical Cone

b) (x - z)^2 + z^2 + zx = 0

(x - z)^2 = - z(x + z)

This dies not give any Surface Equation