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 :
Step-by-step explanation:
1)The given equations are:
x − 2y = 6 ...(i)
3x − 6y = 0 ...(ii)
Putting x = 0 in equation (i) we get
=> 0 - 2y = 6
=> y = -3
x = 0, y = -3
Putting y = 0 in equation (i) we get
⇒x-2×0=6
⇒x=6
x = 6, y = 0
Use the following table to draw the graph
x 0 6
y -3 0
Plotting the two points A(0, -3) and B(6,0) equaion (1) can be drawn
Graph of the equation ..(ii)
3x - 6y = 0 ...(ii)
Putting x = 0 in equation (ii) we get
⇒3×0-6y=0
=> y = 0
x = 0, y = 0
Putting x = 2 in equation (2) we get
⇒3×2-6y=0
=> y = 1
x = 2, y = 1
Use the following table to draw the graph.
x 0 2
y 0 1
Draw the graph by plotting the two points O(0,0) and D(2,1) from table
We see that the two lines are parallel, so they won’t intersect
Hence there is no solution
2)
Answer:
315in^2
Step-by-step explanation:
