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
For the first question:
This is how to get the equation of the ellipse, given those what you have given:
Visualizing the problem above:
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:
Foe the second question......you can answer it easily....Cheers!
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For the first question:
This is how to get the equation of the ellipse, given those what you have given:
Visualizing the problem above:
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:
Foe the second question......you can answer it easily....Cheers!
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