The radius of the circle is the distance between its center and a point that it passes through. This radius can be calculated using the distance formula:

.

Setting :

The area of a circle can be calculated by substituting 10 for in the equation

,

the correct response.

We must first rewrite the equation of the circle in standard form

;

will be the radius.

Subtract 9 from both sides, and rearrange the terms remaining on the left as follows:

Note that blanks have been inserted after the linear terms. In these blanks, complete two perfect square trinomials by dividing linear coefficients by 2 and squaring:

Add to both sides, as follows:

Rewrite the expression on the left as the sum of the squares of two binomials.

The equation is now in standard form.

The area of this circle can be found using this formula:

,

the correct response.

The x-intercept and y-intercept of the line of an equation can be found by substituting 0 for and , respectively, as follows:

x-intercept:

Substitute and simplify:

Solve for by dividing by 2 on both sides:

The x-intercept of the line is located at

The y-intercept can be found by setting and solving for in a similar fashion:

The y-intercept is located at .

The midpoint of a line segment, given its endpoints and , is located at

;

substituting accordingly,

The midpoint is located at .

The midpoint of the line segment between two points 

 and 

is given by the formula

.

Thus, since the line segment is generated by 

 and 

applying the midpoint formula we have

as the midpoint.

Step 1: Recall the midpoint Formula....

, where  is the first point and  is the second point

Step 2: Identify the points and their specific terms...

Step 3: Plug in the values into the midpoint formula...

Simplify...

Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring .

The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so

We can set the lengths of the opposite and adjacent legs to and 5, respectively. The length of the hypotenuse can be determined using the Pythagorean Theorem:

The sine of the angle is equal to the ratio of the length opposite leg to that of the hypotenuse, so

.

Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring . The cosine is defined to be the ratio of the length of the adjacent side to that of the hypotenuse, so

We can set the lengths of the adjacent leg and the hypotenuse to and 3, respectively. By the Pythagorean Theorem, the length of the opposite leg is

The sine of the angle is equal to the ratio of the length of the opposite leg to that of the hypotenuse, so

.

Suppose we allow be the lengths of the opposite leg and adjacent leg and the hypotenuse, respectively, of the right triangle with an acute angle measuring .

The tangent of the angle is the ratio of the length of the opposite leg to that of the adjacent leg, so

We can set the lengths of the opposite and adjacent legs to and 5, respectively. The length of the hypotenuse can be determined using the Pythagorean Theorem:

The cosine of the angle is equal to the ratio of the length of the adjacent leg to that of the hypotenuse, so

.

An identity of trigonometry is

for any value of .

Since , it immediately follows that .

This response is not among the given choices.

The area of a right triangle is half the product of the lengths of its legs, which here are  and  - that is, 

We are given that .  is the leg opposite the angle  and  is its adjacent leg, we can find  using the tangent ratio:

Setting  and , we get

Solve for  by multiplying both sides by 12:

Now, set  and  in the area formula:

,

the correct choice.