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3 years ago

Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).

Mathematics

1 answer:

wolverine [178]3 years ago

3 0

Answer:

y² / 81 - x² / 19 = 1

Step-by-step explanation: See Annex ( vertices and foci in coordinates axis)

The equation in standard form for the hyperbola is:

x² / a² - y²/b² = 1 or y²/a² - x² / b² = 1

In cases of transverse axis parallel to x axis or y axis respectively.

As per given information in this case hyperbola has a transverse axis parallel to y axis the equation is

y²/a² - x² / b² = 1

a is a distance between center and vertex therefore a = 9

c is a distance between center and a focus c = 10

and b will be:

c² = a² + b² ⇒ b² = c² - a² ⇒ b² = (10)² - (9)² ⇒ b² = 100 - 81

b = √19

And the equation in standard form is:

y² / a² - x² / b² = 1

y² / ( 9 )² - x² / √(19)² ⇒ y² / 81 - x² / 19 = 1

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Step-by-step explanation:

You need to remember the following:

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$A_{t3}=A_{t4}=13.6\ in^2$

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<h3>What is distance?</h3>

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Sandra rode her bike 5 times as many miles as Barbara. If b, the distance Barbara rode, equals 3.4 miles.

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