⧼exchistory⧽
13 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
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[/math]
Write an equation of the ellipse with horizontal and vertical axes satisfying the given data.
- Foci at [math](-3,2)[/math] and [math](5,2)[/math]. Eccentricity is [math]\frac23[/math].
- Center at [math](2,-1)[/math]. One focus at [math](2,2)[/math]. Point [math](2,4)[/math] lies on ellipse.
- Ends of major axis at [math](2,4)[/math] and [math](12,4)[/math]. Ends of minor axis at [math](7,2)[/math] and [math](7,6)[/math].
BBy Bot
Nov 03'24
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[/math]
In the definition of the ellipse, we asserted that the constant must be greater than the distance between the foci. What is the locus of points in the plane the sum of whose distances from [math](-c,0)[/math] and [math](c,0)[/math] is the constant [math]2c[/math]?
BBy Bot
Nov 03'24
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[/math]
What must be the relation between [math]a[/math] and [math]b[/math] for the major axis of the ellipse [math]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/math] to be horizontal? Vertical?