You've provided the equation \( x^2 + y^2 = 100 \) and the number 3. It seems like you may want to find specific solutions or explore the relationship between the equation and the number 3.

Let me clarify the situation before proceeding. Are you:
1. Looking for points on the circle where \( x = 3 \) or \( y = 3 \)?
2. Asking for the equation of the circle and interpreting the number 3 in some way?
3. Solving for \( y \) when \( x = 3 \)?
4. Exploring specific properties of this equation with respect to 3 (like radius or points)?
5. Referring to a different context for the number 3 (maybe a parameter)?

### Based on \( x = 3 \), we can find \( y \) values:
We know:
\[
x^2 + y^2 = 100
\]
Substitute \( x = 3 \):
\[
3^2 + y^2 = 100
\]
\[
9 + y^2 = 100
\]
\[
y^2 = 100 - 9 = 91
\]
\[
y = \pm \sqrt{91} \approx \pm 9.53
\]
Thus, the points \( (3, 9.53) \) and \( (3, -9.53) \) are on the circle.

Would you like to go into further detail, or does this help clarify your question? Let me know!

### 5 Related Questions:
1. What is the general equation for a circle, and how does this one compare?
2. How do you solve for \( y \) in terms of \( x \) for this circle?
3. What are the intercepts of this circle on the axes?
4. How do you find the radius of a circle given its equation?
5. How would you graph this circle?

### Tip:
To determine whether a point lies on a circle, simply substitute the coordinates into the circle's equation.

Learn how to find the coordinates on the circle defined by the equation x^2 + y^2 = 100 when x = 3. This solution covers key concepts in geometry, including the equation of a circle and using the Pythagorean Theorem to find points. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation