Answer: (x + 6)² + (y + 5)² = 17
Explanation:
1) The equation of a circle is: (x - a)² + (y - b)² = r², wnere:
a is the x-coordinate of the center of the circleb is the y-coordinate of the center of the circler is the radius of the circle
2) Since the points (-7,-1) and (-5,9) define a diameter, you can find the center of the circle as the mid point of the diameter:
x-coordinate of the mid point = (-7 - 5) / 2 = - 12 / 2 = - 6
y-coordinate of the mid point = (-9 - 1)/ 2 = - 10 / 2 = - 5
Therefore, the center of the circle is (-6,-5)
3) The radius of the center is half the diameter.
The length of the diameter is found using the formula for the distance between two points applied to the two endopoints given:
diameter² = (7 - 5)² + (- 1 + 9)² = 2² + 8² = 4 + 64 = 68
⇒diameter = √68 = 2√17
⇒ radius = diamter / 2 = 2√17 / 2 = √17
4) Now you can replace the coordinates of the center and the radius into the equation:
(x + 6)² + (y + 5)² = 17
34255 = 5 * 13 * 17 * 31
203515 = 5 * 13 * 31 * 101
So GCD(34255, 203515) = 5 * 13 * 31 = 2015
I am not going to tell you the answer but i can tell you how to find it out. First you have to put 19/38 on a paper. Then multipy the numarator and denomanator by the same number on the top and bottom which is called a whole number. 19/38 times 2/2 or 3/3 or 4/4 or anything. Your answer is equivalent to 19/38
