Question

What is the equation for the hyperbola shown?

A. x²/8² - y²/5² = 1

B. x²/5² - y²/8² = 1

C. y²/8² - x²/5² = 1

D. y²/5² - x²/8² = 1

Answer 1

D. y²/5² - x²/8² = 1

Explanation:

A and B are both incorrectly oriented, and D is the only hyperbola that contains the points (0,5) and (0,-5).

Verification (0,5) and (0,-5) are in the hyperbola:

First replace x and y with corresponding x and y values (We will start with x=0 and y=5)

`(5^(2))/(5^(2))-(0^(2))/(8^(2))=1`

Then simplify.

`(25)/(25)-(0)/(16)=1`

`1-0=1`

`1=1`

If the result is an equation (where both sides are equal to each other) then the original x and y values inputted are valid. The same is true with x and y inputs x=0 and y=-5, or any other point along the hyperbola.

Answer 2

D. y²/5² - x²/8² = 1

Explanation:

From the graph of the hyperbola, we can see that points (0,5) and (0,-5) form part of the hyperbola.

This means that the equation of the hyperbola should be satisfied by these points.

Substituting x=0 and y=5 in the given options:

A. LHS = -1 while RHS = 1

B. LHS =
`\[(-5^(2))/(8^(2))\]` while RHS = 1

C. LHS =
`\[(5^(2))/(8^(2))\]` while RHS = 1

D. LHS = 1 and RHS = 1

So only option D contains the point (0,5).

Now verifying option D for the point (0,-5):

LHS = 1 and RHS = 1

So equation D is the correct equation for the hyperbola.