Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 692: 12

An elliptic cone

Work Step by Step

The equation $$14z^2=3x^2+7y^2$$ can be rewritten as follows $$\left(\frac{z}{1/\sqrt {14}}\right)^{2}=\left(\frac{x}{1/\sqrt 3}\right)^{2}+\left(\frac{y}{1/\sqrt{7}}\right)^{2}$$ which is an equation of an elliptic cone with $a=1/\sqrt{ 3}, b=1/\sqrt{7}, c=1/\sqrt{ 14}$. (See equations on page 691.)

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