Visualizing Area Relationships for the General Form Equation y=x^2 of the Parabola | Steve Wait – October 28, 2021

For a point P_(x,y) on the Parabola in the form y=x², the area x² equals the area of product y and the length of the Latus Rectum.

y = x²

1¹ × y¹ = (1¹ × x¹) × (1¹ × x¹)

x = .5

1¹ × y¹ = (1¹ × .5¹) × (1¹ × .5¹)

1¹ × y¹ = .5¹ × .5¹

y¹ = (.5¹ × .5¹) / 1¹

y¹ = .5² / 1¹

y¹ = .25¹ / 1¹

y¹ = .25¹

y = .25

A GeoGebra animation can be viewed here: Area Relationships of the Parabola – GeoGebra

Tags: parabola