please need help as soon as possible!

Question

Question 1: Identify the value of  and the length of each secant segment.

A.) x = 11; PR = 12; PT = 15

B.) x = 15; PR = 12; PT = 19

C.) x = 15; PR = 19; PT = 12

D.) x = 11; PR = 15; PT = 12

Question 2: Identify the graph of the equation (x+3)² + (y+1)² = 9.

A.)

B.)

C.)

D.)

Please give the explanation and the answer!

Answer 1

Hey Becky!

For question one you can set up an equation to solve for x. The product of the external part and total segment length of one secant line is equal to the external total length the other secant line. In other words:

(PQ)PR = (PS)(PT)

Now substitute the numbers you know:

(5)(5+7) = (4)(4+x)

(5)(12) = 16+4x

60 = 16 + 4x

44 = 4x

11=x

For Question 2 you can determine the shape of the circle by examining different aspects of the equation. For example, the radius (r) is equal to the square root of the constant isolated on the right side of the equation:

r² = √9

r = 3

so the radius of the circle is 3 units in length and the diameter is 6 units in length. Unfortunately, all the circles look to be similar in size so we need to examine the equation further.

The center of the circle can be located to (h,v) where h is the opposite of the number with x.The number with x is positive 3 but you need to take the opposite sign of that so the h value is -3.

For v, we need to take the opposite of the number with y which is -1.

So the center of the circle can be located at (-3,-1)

This matches option C, so I believe that is the answer.

Hope this helps!

Answer 2

1) The secant-secant product theorem says the product of a secant segment and the portion of the secant segment outside the circle equals the product of a different secant segment (originating from the same point) and its portion outside the circle. So, in this case, that's:

PR•PQ = PT•PS

12•5 = (4 + x)4

60 = 16 + 4x

44 = 4x

x = 11 (answer a)

2) the generic form of the equation of a circle is (x - h)² + (y - k)² = r² where the center of the circle is at the point (h, k) and the radius of the circle is r. So, in the case of (x+3)² + (y+1)² = 9, the center is ar (-3, -1) and the radius is 3 (because 3² = 9). That's answer c.