Chapter 10.4, Problem 15AYU

To determine

To find: The right match of each graph with its equation:

a. $\frac{x^2}{4}-y^2=1$

b. $x^2-\frac{y^2}{4}=1$

c. $\frac{y^2}{4}-x²=1$

d. $y²-\frac{x^2}{4}=1$

Answer to Problem 15AYU

Solution:

b. $x^2-\frac{y^2}{4}=1$

Explanation of Solution

Given:

The hyperbola and the options.

Formula used:

Center	Transverse axis	Foci	Vertices	Equation
$\left(0,0\right)$	$x\text{-axis}$	$(\pm c,0)$	$(\pm a,0)$	$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ $b²=c²-a²$

Calculation:

From the given figure we see that, The graph opens to the left and right and the vertices are $\left(\pm 1,0\right)$ and transverse axis is $x\text{-axis}$, hence the equation of the hyperbola is given by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.

$a=1$ implies,

$\frac{x^2}{1}-\frac{y^2}{b^2}=1$ This equation matches with option b.

Option b is correct.