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Given: $3x^{2}+16y^{2}=12$.

Finding the Elements of an Ellipse.

My solution:

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

Therefore:

  1. Semi-major and semi-minor axes: $a=2$ and $b=\frac{\sqrt{3}}{2}$.

  2. Foci of an ellipse: $(\pm c; 0)$? $(-\frac{\sqrt{13}}{2}; 0)$ and $(\frac{\sqrt{13}}{2}; 0)$.

  3. Eccentricity: $b^2=a^2-c^2$; $c=\sqrt{4-\frac{3}{4}}=\frac{\sqrt{13}}{2}$; $e=\frac{\frac{\sqrt{13}}{2}}{2}=\frac{\sqrt{13}}{4}$.

  4. Directrix: $x=\pm\frac{a}{e}=\pm\frac{2}{\frac{\sqrt{13}}{4}}=\pm\frac{8}{\sqrt{13}}$.

Please, tell me, whether is my solution right?

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    I think you've made a small mistake on number **4.** It should be $\pm \frac{8}{\sqrt{13}}$. – 2017-01-25

1 Answers 1

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I think your solution is perfectly right.

Only thing to make it more understandable is find the value of c in part 2.

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    You're right, it's my fault. – 2017-01-25