(x ^ 2)/8 - (y ^ 2)/2 = 1 pada titik ( 2sqrt(3) 1)

Given the equation of the hyperbola:

\[
\frac{x^2}{8} - \frac{y^2}{2} = 1
\]

We need to verify if the point \( (2\sqrt{3}, 1) \) lies on the hyperbola. To do this, we will substitute the coordinates \( x = 2\sqrt{3} \) and \( y = 1 \) into the equation.

### Step 1: Substitute \( x = 2\sqrt{3} \) and \( y = 1 \)

Substituting the values into the equation:

\[
\frac{(2\sqrt{3})^2}{8} - \frac{1^2}{2} = 1
\]

### Step 2: Simplify the equation

- \( (2\sqrt{3})^2 = 4 \times 3 = 12 \)
- \( \frac{12}{8} = \frac{3}{2} \)
- \( 1^2 = 1 \)
- \( \frac{1}{2} = 0.5 \)

Now substitute these back into the equation:

\[
\frac{3}{2} - \frac{1}{2} = 1
\]

\[
1 = 1
\]

### Conclusion:

The point \( (2\sqrt{3}, 1) \) **does** lie on the hyperbola, as it satisfies the given equation.

---

Would you like to explore more details, or do you have any questions?

Here are some related questions for further exploration:

1. What are the foci of the hyperbola \(\frac{x^2}{8} - \frac{y^2}{2} = 1\)?
2. How would the graph of this hyperbola look, and where are the asymptotes?
3. How do we derive the standard equation of a hyperbola?
4. What are the lengths of the axes for this hyperbola?
5. How does this hyperbola compare to a vertically oriented one?

**Tip:** When working with conic sections like hyperbolas, identifying key features such as vertices and asymptotes helps to visualize the graph better.

Verify if the point (2√3, 1) lies on the hyperbola x^2/8 - y^2/2 = 1 using detailed mathematical analysis. Understand the equation of a hyperbola and its application in coordinate geometry. Suitable for Grades 10-12 students and those interested in conic sections.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation