https://file.aiquickdraw.com/mathbot/file/1727308209293zxyhbc8u.jpg

The equation given in the image is an equation of an ellipse:

\[
\frac{x^2}{16} + \frac{y^2}{4} = 1
\]

The problem asks for the point \((-2, \sqrt{3})\) to be substituted into this equation to verify whether it lies on the ellipse.

### Steps to solve:
1. Substituting \(x = -2\) and \(y = \sqrt{3}\) into the equation.

\[
\frac{(-2)^2}{16} + \frac{(\sqrt{3})^2}{4} = 1
\]

2. Simplifying the terms:
   - \((-2)^2 = 4\), so \(\frac{4}{16} = \frac{1}{4}\)
   - \((\sqrt{3})^2 = 3\), so \(\frac{3}{4}\)

3. Now, adding these results:
\[
\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1
\]

Since the left-hand side equals the right-hand side, the point \((-2, \sqrt{3})\) **does lie on the ellipse**.

Would you like more details on how ellipses work, or do you have any other questions?

### Related Questions:
1. How do you find the foci of an ellipse given its equation?
2. What is the general form of the equation of an ellipse?
3. How do you determine the major and minor axes of an ellipse from its equation?
4. How do you graph an ellipse using its equation?
5. How do changes in the denominators affect the shape of the ellipse?

**Tip:** Always check if a point satisfies the equation of an ellipse by substituting its coordinates directly into the equation.

Verify if the point (-2, √3) lies on the ellipse given by the equation (x^2)/16 + (y^2)/4 = 1.

Learn how to verify if the point (-2, √3) lies on the ellipse with the equation (x^2)/16 + (y^2)/4 = 1. Step-by-step solution provided, covering concepts from analytic geometry. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation