GRAPHING CIRCLES, PARABOLAS, AND HYPERBOLAS USING SECOND-ORDER LINEAR EQUATIONS IN EXCEL: Second-order equation, circle, parabola, hyperbola, center, radius, geometric shapes, mathematical formula, graphs.

Second-order equation, circle, parabola, hyperbola, center, radius, geometric shapes, mathematical formula, graphs.

Abstract

Abstract: Second-order linear equations in the plane, i.e., geometric shapes such as circles, parabolas, and hyperbolas, are of significant importance in mathematical and scientific research, as well as in various other fields. The graphs of these shapes are used to model natural phenomena, the motion of mechanical and optical systems, and engineering and astronomy problems. Visualizing these shapes using Excel or other graphing software helps in understanding their properties more clearly.