The parametric representation of a point on t | vedclass

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Question

(A) The distance between the two foci is $2ae = 7 - (-1) = 8$. Since $e = 1/2$,we have $2a(1/2) = 8$,which implies $a = 8$. The center of the ellipse

Vedclass · Accepted Answer

$(3+8 \cos 	heta, 4 \sqrt{3} \sin 	heta)$

Vedclass · Answer

(A) The distance between the two foci is $2ae = 7 - (-1) = 8$. Since $e = 1/2$,we have $2a(1/2) = 8$,which implies $a = 8$. The center of the ellipse is the midpoint of the foci: $(\frac{-1+7}{2}, \frac{0+0}{2}) = (3, 0)$. Using $b^2 = a^2(1 - e^2)$,we get $b^2 = 64(1 - 1/4) = 64(3/4) = 48$. Thus,$b = \sqrt{48} = 4\sqrt{3}$. The equation of the ellipse is $\frac{(x-3)^2}{8^2} + \frac{y^2}{(4\sqrt{3})^2} = 1$. The parametric coordinates are given by $(x, y) = (h + a \cos 	heta, k + b \sin 	heta)$,where $(h, k)$ is the center. Substituting the values,we get $(3 + 8 \cos 	heta, 4\sqrt{3} \sin 	heta)$.

The parametric representation of a point on the ellipse whose foci are $(-1,0)$ and $(7,0)$ and eccentricity $1/2$ is

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