Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Ask your questions and receive precise answers from experienced professionals across different disciplines. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

The light from a lamp creates a shadow on a wall with a hyperbolic border. Find the equation of the border if the distance between the vertices is inches and the foci are inches from the vertices. Assume the center of the hyperbola is at the origin.

Sagot :

nuhulawal20

This question is incomplete, the complete question is;

The light from a lamp creates a shadow on a wall with a hyperbolic border. Find the equation of the border if the distance between the vertices is 18 inches and the foci are 4 inches from the vertices. Assume the center of the hyperbola is at the origin.

Answer:

the equation of the border is x²/81 - y²/88 = 1

Step-by-step explanation:

Given the data in the question;

distance between vertices = 2a = 18 in

so

a = 18/2 = 9 in

distance of foci from vertices = 4 in

hence distance between two foci = 2c = 18 + 4 + 4 =  26

so

c = 26/2 = 13 in

Now, from Pythagorean theorem

b = √( c² - a² )

we substitute

b = √( (13)² - (9)² ) = √( 169 - 81 ) = √88

we know center is at the origin, so

( h, k ) = ( 0, 0 )

h = 0

k = 0

Using equation of hyperbola

[ ( x-h )² / a² ] - [ ( y - k )² / b² = 1

we substitute

[ ( x-0 )² / 9² ] - [ ( y - 0 )² / (√88)² ] = 1

x²/81 - y²/88 = 1

Therefore, the equation of the border is x²/81 - y²/88 = 1

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.