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KonstantinChe [14]
3 years ago
11

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ±five divided by four times

x..
Mathematics
1 answer:
Vinvika [58]3 years ago
5 0

Answer:

The equation of the hyperbola in standard form is

\frac{y^{2}}{100}-\frac{4x^{2}}{625}=1

Step-by-step explanation:

* We will take about the standard form equation of the hyperbola

- If the given coordinates of the vertices (0 , a) and (0 , -a)

∴ The transverse axis is the y-axis. (because x = 0)

- If the given asymptotes at y = ± (b/a) x

∴  Use the standard form  ⇒ y²/a² - x²/b² = 1

* Lets use this to solve our problem

∵ The vertices are (0 , 10) and (0 , -10)

∴ a = ±10

∴ a² = 100

∵ The asymptotes at y = ± 5/4 x

∴ ± 5/4 = ± b/a

∵ a = ± 10

∴ ± 5/4 = ± b/10 ⇒ using cross multiplication

∴± (4b) = ± (5 × 10) = ± 50 ⇒ divide both sides by 4

∴ b = ± 25/2

∴ b² = 625/4

* Now Lets write the equation

* y²/100 - x²/(625/4) = 1

∵ x² ÷ 625/4 = x² × 4/625 = (4x²/625)

∴ y²/100 - 4x²/625 = 1

* The equation of the hyperbola in standard form is

  \frac{y^{2}}{100}-\frac{4x^{2}}{625}=1

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2 years ago
5) Consider the equation : y=7x+8
vekshin1

The correct students about the function are;

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C: The function y = 7x + 8 has the greatest  y-intercept.

<h3>How to Interpret the Function Table?</h3>

We are looking at the equation;

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4 0
10 months ago
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Artist 52 [7]
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Determine the slope and the y-intercept of the line represented by the equation y= -7/3×+3 slope: 7/9 ;y-intercept: 3 slope: 9/7
Mademuasel [1]

Answer:

slope ⟹ \:  -  \frac{7}{9}  \\ y  \:  intercept⟹ \: 3

Step-by-step explanation:

The standard form of this equation is

y = mx + c \\

m stands for the gradient or the slope, and c represents the y-intercept

y = mx + c \\ y =  -  \frac{7}{9} x + 3 \\ m =  -  \frac{7}{9}  \:  \\ and \:   \\  \: y \: intercept \:  = 3

7 0
2 years ago
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