Show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x Video Lesson

About This Video

Curriculum-aligned Grade 10 Mathematics lesson video for Show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x. Use it for classroom preview, instruction support, or home review.

This watch page is dedicated to the video. For the complete text lesson plan, activities, standards alignment, and answer guides, use the companion lesson page: Show that the equation of a circle with center at the origin and radius r is x2 + y2 = r2 and determine the equation for the graph of a circle with radius r and center (h, k), (x lesson plan.

Video Learning Notes

In this lesson, students learned that a circle is the set of all points at a fixed distance (radius) from a center point. They showed that the equation of a circle centered at the origin with radius r is \(x^2 + y^2 = r^2\), and generalized this to any center (h, k) with the equation \((x - h)^2 + (y - k)^2 = r^2\). Students practiced writing these equations and graphing circles on the coordinate plane, connecting geometric definitions with algebraic representations.

Learning Goals

• Explain why the equation of a circle with center at the origin and radius r is x2 + y2 = r2.
• Determine the equation of a circle with radius r and center at any point (h, k) as (x - h)2 + (y - k)2 = r2.
• Apply the equations of circles to graph circles on the coordinate plane.

Curriculum Context

Grade: Grade 10

Subject: Mathematics

Curriculum: TEKS