Assertion: ellipse's equation | /r/CapableOf | represent ellipse
Facets:
value: always
type: TEMPORAL
value: with axes
type: OTHER
Source sentences:
text: The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes.
text: Prove that this parametric equation forms an ellipse except when $\theta = 0 $ and $\pi$ .
text: Must such an equation always represent an ellipse?
text: if B 2 − 4 AC < 0 , the equation represents an ellipse; if A = C and B = 0 , the equation represents a circle, which is a special case of an ellipse;
text: , the equation represents an ellipse; if B 2 − 4 AC = 0 , the equation represents a parabola;
text: Every equation of that form represents an ellipse if A not equal B and A · B > 0 that is, if the square terms have unequal coefficients, but the same signs.
text: We now start by first writing down the basic equations representing an ellipse.
text: Since the coefficients of the x 2 and y 2 terms are unequal and both positive, this equation might represent an ellipse.
text: This equation represents an ellipse having center at (2,− 3) and graph as shown in Figure 3.46.
text: Otherwise, assuming the equation represents either a non-degenerate hyperbola or ellipse, the eccentricity is given by