The equation of the hyperbola is :
The center of a hyperbola is located at the origin that means at (0, 0) and one of the focus is at (-50, 0)
As both center and the focus are lying on the x-axis, so the hyperbola is a horizontal hyperbola and the standard equation of horizontal hyperbola when center is at origin:
The distance from center to focus is 'c' and here focus is at (-50,0)
So, c= 50
Now if the distance from center to the directrix line is 'd', then
Here the directrix line is given as : x= 2304/50
Thus,
⇒
⇒ a² = 2304
⇒ a = √2304 = 48
For hyperbola, b² = c² - a²
⇒ b² = 50² - 48² (By plugging c=50 and a = 48)
⇒ b² = 2500 - 2304
⇒ b² = 196
⇒ b = √196 = 14
So, the equation of the hyperbola is :
Answer:
The first six terms of this arithmetic sequence are: 30, 32, 34, 36, 38, 40
Step-by-step explanation:
The nth term of an arithmetic sequence is given by:
In which d is the common difference, that is, each term is increased by d.
d = 2, Po= 30
First term is 30, each consecutive is increased by 2. So
30, 32, 34, 36, 38, 40