Pre Calculus: Finding the Equation of the Circle Given the Radius and Center

Introduction to the Standard Form and First Example00:00:02

The video introduces the standard form of the equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. The first example demonstrates how to find the equation given a center of (-4, -5) and a radius of 5.

Solving the First Example00:01:06

The values are plugged into the standard form. When h or k are negative, they are enclosed in parentheses. The equation simplifies to (x + 4)^2 + (y + 5)^2 = 25, which is the standard form of the circle for the given center and radius.

Second Example: Center (0, 10) and Radius sqrt(2)00:03:01

The video moves to a second example, with the center at (0, 10) and a radius of the square root of 2. The values are substituted into the standard form.

Solving the Second Example00:03:44

x minus 0 simplifies to x, so the term becomes x^2. The y term is (y - 10)^2. For the radius, the square root of 2 squared equals 2. The final equation is x^2 + (y - 10)^2 = 2.

Conclusion and Channel Promotion00:04:19

The presenter concludes the examples and encourages viewers to like, subscribe, and browse for more pre-calculus videos on their channel.