The Ellipsoid $4 x ^ { 2 } + 5 y ^ { 2 } + z ^ { 2 } = 28$

question 34

Short Answer

The ellipsoid $4 x ^ { 2 } + 5 y ^ { 2 } + z ^ { 2 } = 28$ intersects the plane $y = 2$ in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

---

Definitions:

Simplify

The process of making an expression easier to understand or work with by combining like terms, reducing fractions, etc.

Rational Model

A mathematical model that uses rational expressions to describe relationships between different quantities.

Least Common Denominator

The smallest positive integer that is divisible by each denominator of a set of fractions, facilitating their comparison or summation.

Common Denominator

The shared multiple of the denominators of two or more fractions, used to make their denominators the same for addition or subtraction.