Find the equation of a parabola with focus (3, 4) and directrix y = 1.
2 answers:
Refer to the diagram shown below.
At an arbitrary point P (x,y) on the parabola, the distance, d, from the focus to P should be equal to the distance from P to the directrix.
That is,
d² = (x - 3)² + (y - 4)² = (y - 1)²
(x - 3)² + y² - 8y + 16 = y² - 2y + 1
(x - 3)² + 15 = 6y
Divide each side by 6 to obtain
y = (1/6) (x - 3)² + 5/2
The vertex of the parabola is at (3, 5/2).
The line of symmetry is x = 3.
The leading coefficient, 1/6, is positive, therefore the curve opens upward.
Answer:
At an arbitrary point P (x,y) on the parabola, the distance, d, from the focus to P should be equal to the distance from P to the directrix.
That is,
d² = (x - 3)² + (y - 4)² = (y - 1)²
(x - 3)² + y² - 8y + 16 = y² - 2y + 1
(x - 3)² + 15 = 6y
Divide each side by 6 to obtain
y = (1/6) (x - 3)² + 5/2
The vertex of the parabola is at (3, 5/2).
The line of symmetry is x = 3.
The leading coefficient, 1/6, is positive, therefore the curve opens upward.
Answer:
You might be interested in
Answer:
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
- By definition, the perimeter of the figure is the sum of the lenght of each side. Then, you must make the addition as following:
Where is the perimeter of the figure.
- Add the like terms, then, you obtain the following expression in simplest form:
Answer:
6
Step-by-step explanation:
The maximum value of the sin function is at , when sin is equal to 1. Since you need to multiply pi/12 by 6 to get to pi/2, the maximum amount of people will be at the square after 6 hours. Hope this helps!