Math Problem Statement

Give the equation of the circle centered at the origin and passing through the point (0, 10).

Solution

To find the equation of a circle centered at the origin (0,0)(0, 0) and passing through the point (0,10)(0, 10), we can use the standard form of a circle equation:

x2+y2=r2x^2 + y^2 = r^2

Since the circle passes through (0,10)(0, 10), the radius rr is the distance from the origin to this point, which is 1010.

Thus, the equation of the circle is:

x2+y2=102x^2 + y^2 = 10^2

Simplifying, we get:

x2+y2=100x^2 + y^2 = 100

Would you like a detailed explanation? Here are some related questions:

  1. What is the general equation for a circle centered at any point (h,k)(h, k)?
  2. How do you find the radius of a circle when given two points on its diameter?
  3. What if the circle passed through a different point, like (5,5)(5, 5)?
  4. Can this method be used for circles not centered at the origin?
  5. How do you graph a circle equation?

Tip: Always check if the point given is on the circle by substituting it into the equation.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Equation of a Circle

Formulas

x^2 + y^2 = r^2

Theorems

Distance Formula

Suitable Grade Level

Grades 9-10