Math Problem Statement

x^2+y^2=100 $$$$ $$$$ 3

Solution

You've provided the equation x2+y2=100x^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=3x = 3 or y=3y = 3?
  2. Asking for the equation of the circle and interpreting the number 3 in some way?
  3. Solving for yy when x=3x = 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=3x = 3, we can find yy values:

We know: x2+y2=100x^2 + y^2 = 100 Substitute x=3x = 3: 32+y2=1003^2 + y^2 = 100 9+y2=1009 + y^2 = 100 y2=1009=91y^2 = 100 - 9 = 91 y=±91±9.53y = \pm \sqrt{91} \approx \pm 9.53 Thus, the points (3,9.53)(3, 9.53) and (3,9.53)(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 yy in terms of xx 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.

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Math Problem Analysis

Mathematical Concepts

Geometry
Analytic Geometry
Equations of Circles

Formulas

Equation of a circle: x^2 + y^2 = r^2
Solving for y: y = ±√(r^2 - x^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-12