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Conics - Circle

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Integrated Math II

41. CC.HSG.GPE.A.1

41.1 Conics - Circle

Conics - Circle: Equation, Standard Form, and Graphing

Master the standard form equation of a circle, convert from general form, and graph any circle once you know its center and radius.

What You'll Learn

Identify the standard form equation of a circle as (x minus h) squared plus (y minus k) squared equals r squared

Locate the center (h, k) and radius r directly from an equation written in standard form

Derive the circle equation from the distance formula between the center and any point on the circle

Convert an equation from general form to standard form by completing the square on x and y

Apply the midpoint formula to find a circle's center when given the endpoints of a diameter

Graph a circle by plotting the center and marking points a distance r away in four directions

What You'll Practice

Sketching circles from conic form equations with given centers and radii

Converting between standard form and conic form using algebraic manipulation

Finding circle equations given center coordinates and radius values

Calculating radius using distance formula between two points

Writing equations for circles tangent to lines using perpendicular slopes

Why This Matters

Understanding circles in conic form is essential for advanced algebra and calculus. You'll use these skills to analyze circular motion, optimize distances, and solve real-world problems involving ranges, signals, and geometric constraints in engineering and physics.

Before You Start — Make Sure You Can:

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)Midpoint formula: \(M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)\)Conics - Ellipse

This Unit Includes

8 Video lessons

Practice exercises

Learning resources

Skills

Conic Sections

Circle Equations

Completing the Square

Distance Formula

Midpoint Formula

Radius and Center

Tangent Lines

Perpendicular Slopes

OH Curriculum Aligned