Answer:
x squared over 4 plus y squared over 8 equals 1
Step-by-step explanation:
The general equation of ellipse is given as;
(x²/a²) + (y²/b²) = 1
The coordinates of a foci are: (±c, 0) where;
c² = b² - a²
However, we know that equation of directrix is; x = ±a/e
Now, Directrix is given ±4
Thus, a/e = 4
a = 4e
We also know that c = ae from ellipse foci coordinates.
Thus, ae = 2
since ae = 2, then (4e)e = 2
4e² = 2
e² = 2/4
e = 1/2
Thus;
a = 4 × 1/2
a = 2
Since c² = b² - a²;
2² = b² - 2²
4 = b² - 4
b² = 8
From (x²/a²) + (y²/b²) = 1, we can put our values to get;
x²/4 + y²/8 = 1
Okay so you have to set it up as 3.1 over 1.35 and 37.75 over x then you solve for that by doing 37.75 times 1.35 which is 50.9625 and then divide by 3.1 and you get 16.4
The slope of the line is 4/1 and the y-intercept is -1.
3(8-4x) < 5(x-5)
24-12x < 5x-25
-12x-5x < -25 -24
-17x < -49
x > ⁴⁹/₁₇
