Answer: p = 4, r = 4
<u>Step-by-step explanation:</u>
The equation of a circle is: (x - h)² + (y - k)² = r² where
- (h, k) is the center of the circle
- r is the radius of the circle
Complete the square:
x² - 10x + _____ + y² + py + _____ = -13 + ___ + ___
x² - 10x + <u> (-10/2)² </u> + y² + py + <u> (p/2)²</u> = -13 + <u> (-10/2)² </u> + <u> (p/2)²</u>
(x - 5)² + (y + p/2)² = -13 + 25 + (p/2)²
↓ ↓ |_____<u>↓</u>_____|
h = 5 k = -p/2 r²
Given: (h, k) = (5, -2)
-2 = -p/2
-4 = -p
4 = p
r² = -13 + 25 + (p/2)²
= -13 + 25 + (4/2)²
= -13 + 25 + 4
= 16
r = 4
The answer is 3283
in word form its three thousand, two hundred, eighty three
Answer:
Step-by-step explanation:
<u>Perpendicular Bisector</u>
The bisector of a segment defined by points (x1,y1) and (x2,y2) must pass by the midpoint of the segment.
The midpoint (xm,ym) is calculated as follows:
The endpoints of the segment are (-3,-8) and (5,-4), thus the midpoint M is:
Midpoint: M(1,-6)
Let's find the slope of the given segment. The slope can be calculated with the formula:
If the bisector is also perpendicular, its slope m2 and the slope of the segment m1 must comply:
Solving for m2:
Once we have the slope -2 and the point through which our line must pass (1,-6), we compute the equation in its point-slope form:
Operating
Rearranging
You can simplify the fraction to get 2/5. If you convert this into a decimal you will get 0.4, so D is your answer.
