Finding the Points of intersection between the Circle and a Line

Introduction and Method00:00:00

Explanation of the concept of intersection between a line and a circle, identifying that simultaneous equations are the required mathematical process.

Setting up the Simultaneous Equation00:00:37

The process of rearranging the linear equation for one variable and substituting it into the circle's equation.

Expanding and Simplifying00:01:37

Expansion of the algebraic terms and simplification of the resulting equation to isolate the quadratic expression.

Solving for Y Coordinates00:02:51

Factorization of the simplified equation and the use of the difference of two squares to determine the two possible Y coordinate values.

Calculating Corresponding X Coordinates00:03:45

Substitution of the Y values back into the rearranged linear equation to find the corresponding X coordinates, resulting in the final intersection points.