The general form of a parabola when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus. We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus. Remember that the parabola will hug the focus and run away from the directrix. The formula would be slightly different if the parabola was opening either left or right.
Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix. The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2. We can now write the equation of the parabola:
(x + 2)² = 4(2)(y - 2)
(x + 2)² = 8(y - 2) Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'
-2x + 12 = 2y
Add 2x on both sides,
12 = 2y + 2x
Divide by 2 on both sides,
6 = y + x -> x + y = 6
The answer is D.
Hello!
You can use the Pythagorean Theorem to solve this
c is the hypotenuse
a and b are the legs
Put in the values you know
Square the numbers
Subtract 2.25 from both sides
Take the square root of both sides
b = 0.8
The answer is 0.8km
Hope this helps!
What are the answer choices in the drop down?
Answer:
the answer to number one is (13.3,2)
the answer to number two is (2,-2)
Step-by-step explanation:
