conic sections:ellipse

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Dean Carl Manansala's picture
conic sections:ellipse

questions:find teh equation of the ellipse satisfying the following conditions
1. foci at (±2,0),one vertex at (3,0)

2. co-vertices (-4,3) and (-4,-5),eccentricity 3/5

8eightI'sD's picture
For the first question:

For the first question:

This is how to get the equation of the ellipse, given those what you have given:

Visualizing the problem above:

uto.png

We see that $a^2 = b^2 + c^2$, then $(3)^2 = b^2 + (2)^2,$ then
$b = \sqrt{5}$

Since we know that the center is $C(x,y) = C(0,0),$ we can now get the equation of
the ellipse:

$$\frac{x^2}{a^2} +\frac{y^2}{b^2} = 1$$ $$\frac{x^2}{(3)^2} +\frac{y^2}{(\sqrt{5})^2} = 1$$ $$\frac{x^2}{9} +\frac{y^2}{5} = 1$$

We can now lable the ellipse that is described by the poster:

final_uto.png

Foe the second question......you can answer it easily....Cheers!

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