Answer:
In order to begin figuring that out, we need to know about the equation.
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
Answer:
vertex: (2,-18)
Step-by-step explanation:
y = ax² + bx + c
(-1,0) : a - b + c = 0 ...(1)
(5,0) : 25a +5b +c = 0 ...(2)
(0,-10): 0a + 0b + c = -10 c=-10
(1) x5: 5a - 5b + 5c = 0 ...(3)
(2)+(3): 30a + 6c = 0 30a = -6c = 60 a = 2
(1): 2 - b -10 = 0 b = -8
Equation: y = 2x² - 8x -10 = 2 (x² -4x +4) - 18 = 2(x-2)² -18
equation: y = a(x-h)²+k (h,k): vertex
vertex: (2,-18)
1st) reflection over the point G
2nd) a dilation of 1/2 with fixed point G
3rd) a traslation 2 units left and 4 units up
