a Let's recall the properties of an ellipse with center

(0, 0) .

Properties of Horizontal Ellipses
$\underline{Standard Equation} \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 a > b > 0$	Major Axis $Horizontal$	Vertices $(\pm a, 0)$	Co-vertices $(0, \pm b)$	Foci $(\pm c, 0) on x - axis$
Properties of Vertical Ellipses
$\underline{Standard Equation} \frac{x ^{2}}{b ^{2}} + \frac{y ^{2}}{a ^{2}} = 1 a > b > 0$	Major Axis $Vertical$	Vertices $(0, \pm a)$	Co-vertices $(\pm b, 0)$	Foci $(0, \pm c) on y - axis$

We can see that the given ellipse is a horizontal ellipse. The hole and tee are located at the foci,

(\pm c, 0) .

Therefore, the distance between them will be equal to the value of

2 c .

To determine the value of

c,

we first need to find

a

and

b .

The length of the major axis is

2 a,

and the length of the minor axis is

2 b .

Let's identify the values of

a

and

b .

Major Axis Length = 2 a

$Major Axis Length = 24$

24 = 2 a

$LHS / 2 = RHS / 2$

12 = a

We have identified the value

a = 12 .

Let's identify the value of

b .

Minor Axis Length = 2 b

$Minor Axis Length = 9$

9 = 2 b

$LHS / 2 = RHS / 2$

4.5 = b

Now that we have the values of

a

and

b,

we can use the fact

c^{2} = a^{2} - b^{2}

for an ellipse to determine the value of

c .

c^{2} = a^{2} - b^{2}

$a = 12$ , $b = 4.5$

c^{2} = 12^{2} - 4.5^{2}

Calculate power

c^{2} = 144 - 20.25

Subtract terms

c^{2} = 123.75

$LHS = RHS$

c^{2} = 123.75

Calculate root

c \approx 11.124

Finally, using the value of

c = 11.124,

we can determine the distance between the hole and tee.

Distance = 2 c ⇕ 2 (11.124) \approx 22.25 feet

{{ 'ml-heading-exercise' | message }} {{ exercise.name }} {{ 'ml-label-page' | message }} {{ exercise.page }}