{I really need this answered-} Which value of M makes the inequality 1/4m > 3 true?

select all correct values

A. M = 0

B. M = 4 3/5

C. M= 12

D. M = 12 1/5

E. M = 20

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Ответ:

dbag1162

06.06.2022

Mathematics

x squared over 8 plus y squared over 4 equals 1

Step-by-step explanation:

The general equation of ellipse is given by :-

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

For foci =(c,0) , and a>b we have c^2=a^2-b^2 .

Given, For an ellipse , we have

Directrix at x = ±4 and foci at (2, 0) and (−2, 0).

Since, directrix = $\pm\dfrac{a}{e}$ and $foci =(\pm ae,0)$ , where e is the eccentricity.

That means

$\dfrac{a}{e}=4\ \ \ \&\ \ ae=2\\\\\Rightarrow\ e=\dfrac{a}{4}\ \&\ \ ae=2\\\\\Rightarrow\ a(\dfrac{a}{4})=2\\\\\Rightarrow\ a^2=8\\\\\Rightarrow\ a=\pm2\sqrt{2}$

Also,

$c^2=a^2-b^2\\\\\Rightarrow\ 2^2= (2\sqrt{2})^2-b^2\\\\\Rightarrow\ b^2=8-4=4\\\\\Rightarrow\ b^2=4$

So, the equation of ellipse becomes

$\dfrac{x^2}{8}+\dfrac{y^2}{4}=1$

hence, the correct option is $\dfrac{x^2}{8}+\dfrac{y^2}{4}=1$ .

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{I really need this answered-} Which value of M makes the inequality 1/4m > 3 true?select all correct valuesA. M = 0B. M = 4 3/5C. M= 12D. M = 12 1/5E. M = 20​