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# The ellipse x^2/49+y^2/b^2=1 has foci at (5,0) and (-5,0).

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The ellipse x^2/49+y^2/b^2=1 has foci at (5,0) and (-5,0).

(a) Fimd the length of a semi major axis of this ellipse

(b)compute the value of b

Feb 17, 2021

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The foci of an ellipse are at $$(\pm c, 0)$$ if the equation of the ellipse is $$\frac{x^2}{49} + \frac{y^2}{b^2} = 1$$.

That means that c = 5 and $$b=\sqrt{49-25}=2\sqrt{6}.$$

The length of the semi-major axis is $$2b = 4\sqrt{6}$$

Feb 20, 2021