Find the equation of the ellipse whose foci are at 0- - 4 and e -4-5-

Clearly, the major axis lies along the y axis. Let the required equation be x^2/b^2+y^2/a^2=1. Here, c=4 and e=4/5. so, a=c/e=5. ∴ b^2=(a^2 c^2)=(25 16)=9. ...

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Standard XI

Mathematics

Standard Form of an Ellipse

Find the equa...

Question

Find the equation of the ellipse whose foci are at $(0, \pm 4)$ and $e = \frac{4}{5} .$

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Solution

Clearly, the major axis lies along the y-axis.

Let the required equation be $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1.$

Here, $c = 4$ and $e = \frac{4}{5} .$ so, $a = \frac{c}{e} = 5.$

$∴ b^{2} = (a^{2} - c^{2}) = (25 - 16) = 9.$

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Find the equation of the ellipse whose foci are at (0,±4) and e=45.

Clearly, the major axis lies along the y-axis. Let the required equation be x2b2+y2a2=1. Here, c=4 and e=45. so, a=ce=5. ∴ b2=(a2−c2)=(25−16)=9.

Find the equation of the ellipse whose foci are at $(0, \pm 4)$ and $e = \frac{4}{5} .$

Clearly, the major axis lies along the y-axis.

Let the required equation be $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1.$

Here, $c = 4$ and $e = \frac{4}{5} .$ so, $a = \frac{c}{e} = 5.$

$∴ b^{2} = (a^{2} - c^{2}) = (25 - 16) = 9.$