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

The equation of the hyperbola in standard form is

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

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation: