Convert the line given by the parametric equations to symmetric equations.
Enter the symmetric equations in alphabetic order.

Ask by Phillips Grant. in the United States

Jan 13,2025

Question

Convert the line given by the parametric equations to symmetric equations.
Enter the symmetric equations in alphabetic order.

Ask by Phillips Grant. in the United States

Jan 13,2025

UpStudy AI · Accepted Answer

The given parametric equations are:

$$
\begin{cases}
x(t) = -2 - 2t \
y(t) = 1 - 10t \
z(t) = 5 - 3t
\end{cases}
$$

To convert these to symmetric equations, follow these steps:

1. **Solve each equation for $$ t $$:**

$$
\begin{align*}
t &= \frac{x + 2}{-2} \
t &= \frac{y - 1}{-10} \
t &= \frac{z - 5}{-3}
\end{align*}
$$

2. **Express the equations with positive denominators by multiplying numerator and denominator by $$-1$$:**

$$
\frac{x + 2}{2} = \frac{y - 1}{10} = \frac{z - 5}{3}
$$

3. **Arrange the equations in alphabetical order:**

$$
\frac{x + 2}{2} = \frac{y - 1}{10} = \frac{z - 5}{3}
$$

**Final Symmetric Equations:**

$$
\frac{x + 2}{2} = \frac{y - 1}{10} = \frac{z - 5}{3}
$$
The symmetric equations are: $$ \frac{x + 2}{2} = \frac{y - 1}{10} = \frac{z - 5}{3} $$