For a point P(x,y) on the Parabola in the standard vertex form y = x2, the area x2 equals the area of product y and the length of the Latus Rectum. y=x2{y}={{x}}^{2} 11×y1=(11×x1)×(11×x1)1^{1}\times {{y}}^{1}=\left(1^{1}\times {{x}}^{1}\right)\times \left(1^{1}\times {{x}}^{1}\right) x=.5x=.5 11×y1=(11×.51)×(11×.51)1^{1}\times {{y}}^{1}=\left(1^{1}\times {.5}^{1}\right)\times \left(1^{1}\times .5^{1}\right) 11×y1=.51×.511^{1}\times {{y}}^{1}={.5}^{1}\times {.5}^{1} y1=(.51×.51)11{{y}}^{1}=\frac{\left({.5}^{1}\times {.5}^{1}\right)}{1^{1}} y1=.5211{{y}}^{1}=\frac{{.5}^{2}}{1^{1}} y1=.25111{{y}}^{1}=\frac{{.25}^{1}}{1^{1}} y1=.251{{y}}^{1}={.25}^{1} y=.25y=.25 A GeoGebra animation can be viewed here: Area Relationships of the Parabola – GeoGebra
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