For the ellipse `x^2+4y^2=9` a. the eccentricity is 1/2 b. the latus rectum is 3/2 c. a focus is `(3sqrt(3),0)` d. a directrix is `x=-2sqrt(3)`

Explanation

Given

`x^{2}+4 y^{2}=9 `


`Rightarrow frac{x^{2}}{9}+frac{y^{2}}{frac{9}{4}}=1`


Here, `a>b`


`therefore e=sqrt{1-frac{b^{2}}{a^{2}}} `

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