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: $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$

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

$d= \frac{a^{2}}{c}$

Here the directrix line is given as : x= 2304/50

Thus, $\frac{a^{2}}{c} = \frac{2304}{50}$

⇒ $\frac{a^{2}}{50} = \frac{2304}{50}$

⇒ 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 : $\frac{x^{2}}{48^2} - \frac{y^{2}}{14^2} = 1$

5 0

3 years ago

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The cost of a train ticket increases by

erastova [34]

It costs $122.4 dollars before the increase.

<h3>How to calculate percentage of a number. Use the percentage formula: P% * X = Y</h3>

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 17%, X is 7.20, so the equation is 17% * 7.20 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

Therefore, It costs $122.4 dollars before the increase.

Learn more about Finding the Percentage here:

brainly.com/question/24862040

6 0

2 years ago

What is the axis of symmetry for y=6x^2+6x

Sonja [21]

Answer:

x=3

Step-by-step explanation:

6 0

3 years ago