Episode 19 — Analytical Geometry

Equations of Circles

Learners will be able to:

• Calculate the distance between two points A and B using the formula: √((x2 - x1)² + (y2 - y1)²). • Find the midpoint M of a line segment AB by adding the x values of the endpoints and halving this value, then doing the same with the y values. • Determine the gradient or slope M of a line segment AB by finding the difference between the y values and dividing by the difference between the x values. • Use trigonometry to find the angle of inclination theta of a line given its gradient M. • Identify the equation of a circle in standard form (x² + y² = r²) and use it to determine the center and radius of the circle. • Rewrite an equation of a circle in standard form by completing the square.