19. Conic Sections

Ellipses: Standard Form

객관식
In the context of conic sections, a “completely flat ellipse” corresponds to a degenerate case where the minor axis shrinks to 0 (so $b = 0$ while $a > 0$ ). Using the ellipse eccentricity formula $e = \frac{c}{a}$ with $c^{2} = a^{2} - b^{2}$ , what is the eccentricity of this completely flat ellipse?
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객관식
Given the equation $$\frac{x^2}{4}$+$\frac{y^2}{9}$=1$ , sketch a graph of the ellipse.
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객관식
Given an ellipse centered at the origin with a major axis along the x-axis, a length of 10 for the major axis, and a length of 6 for the minor axis, which equation represents this ellipse?
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객관식
An ellipse is given in standard form by $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ . Which lines are the directrices of the ellipse?
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객관식
Determine the vertices and foci of the following ellipse: $$\frac{x^2}{49}$+$\frac{y^2}{36}$=1$ .
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객관식
Given the ellipse equation $$\frac{x^2}{16}$+$\frac{y^2}{4}$=1$ , determine the magnitude of the semi-major axis (a) and the semi-minor axis (b).
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객관식
Determine the vertices and foci of the following ellipse: $$\frac{x^2}{9}$+$\frac{y^2}{16}$=1$ .
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객관식
The graph of an ellipse is shown with center at $(2, 3)$ , a major axis of length $6$ parallel to the x-axis, and a minor axis of length $4$ . Which equation represents this ellipse?
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객관식
Find the standard form of the equation for an ellipse with the following conditions.
Foci = $$\left$(-5,0$\right$),$\left$(5,0$\right$)$
Vertices = $$\left$(-8,0$\right$),$\left$(8,0$\right$)$
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객관식
Graph the ellipse $$\frac{\left(x-1\right)^2}{9}$+$\frac{\left(y+3\right)^2}{4}$=1$ .
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객관식
Determine the vertices and foci of the ellipse $$\left$(x+1$\right$)^2+$\frac{\left(y-2\right)^2}{4}$=1$ .
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