Assertion: ellipse's point | /r/CapableOf | lie on the ellipse
Facets:
value: thus,
type: MANNER
Source sentences:
text: and as the triangles OMN and ORS are similar, then OM : OR = MN : RS or b : a = PS : RS , so that It proves that the point P (x, y) obtained by the construction lies on the ellipse.
text: Repeat for all other points in the same manner, and the resulting points of intersection will lie on the ellipse.
text: Therefore, any point that satisfies equation (1), i.e. x2/a2 + y2/b2 = 1, lies on the ellipse.
text: Thus, using the condition b2 x 1 2 + a2 y 1 2 = a2b2 , that the point lies on the ellipse, obtained is
text: The constants a and b are specific to a particular ellipse and the variables are the x and y coordinates of points that lie on the ellipse.