https://file.aiquickdraw.com/mathbot/file/1727298983473tpriuomk.jpg

The equation in the image is:

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

This is an equation of an ellipse. You are asked to check whether the point \((-2, \sqrt{3})\) lies on this ellipse.

### To solve:

1. The equation of the ellipse can be written as:

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

2. We substitute the point \((-2, \sqrt{3})\) into the equation:
   - \(x = -2\)
   - \(y = \sqrt{3}\)

Substitute \(x\) and \(y\) into the equation:

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

Simplifying the terms:

\[
\frac{4}{16} + \frac{3}{4} = 1
\]

\[
\frac{1}{4} + \frac{3}{4} = 1
\]

\[
1 = 1
\]

Thus, the point \((-2, \sqrt{3})\) lies on the ellipse because the equation holds true.

Would you like more details or have any questions?

### Related Questions:
1. How do you find the center of an ellipse from its equation?
2. What are the lengths of the major and minor axes of this ellipse?
3. How do you determine the foci of an ellipse given its equation?
4. What is the standard form of an ellipse equation?
5. How do you calculate the eccentricity of this ellipse?

### Tip:
When solving ellipse problems, always compare the equation to the standard form \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) to identify the ellipse's properties.

x^2/16 + y^2/4 = 1, pada titik (-2, √3). Does the point (-2, √3) lie on the ellipse?

Learn how to verify whether the point (-2, √3) lies on the ellipse with the equation x^2/16 + y^2/4 = 1 by substituting values and simplifying. This step-by-step solution demonstrates key concepts in analytic geometry and ellipse equations.

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