The first photo is the problem Homework 2.2.47 needing to be worked out. The fol

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The first photo is the problem Homework 2.2.47 needing to be worked out. The following photos are the examples on how to do the problem. I need the points of intersection. Thank you very much. ew History Bookmarks People Window Help Do Homework -Dylan Mayne Secure: https://www.mathxl.com/Student/PlayerHomework.aspx?homeworkid-461847962&questionld-1; Math 1314.019 College Algebra: Spring 2018 Homework: 2.2 Circles Score: 0 of 1 pt 2.2.47 14 of 16 (15 complete) Find the coordinates of all points whose distance from (-5,0) is 5 and whose distance from (-2,-1) is 5 Find these points. (Use a comma to separate answers as needed.Type ordered pairs.) Enter your answer in the answer box and then click Check Answer All parts showing Clear All

Explanation / Answer

Solution:

The distance of a point (x,y) from another (a,b) is given by sqrt[(x-a)^2 + (y-b)^2].
This means we need a point (x,y) such that:
(x-(-5))2 + (y-(0))2 =5
(x-(-2))2 + (y-(-1))2 =5

or we can say

(x+5)2 + (y)2 =5 and (x+2)2 + (y+1)2 =5

This means (x+5)2 + (y)2 = (x+2)2 + (y+1)2.

So (x+5)2 - (x+2)2 = (y+1)^2 - (y)2,

or (2x+7)(3)=(2y+1)(1) [using formula (a2-b2)=(a+b)(a-b)]

So:
(2x+7)(3)=(2y+1)(1)  
or, 6x +21 = 2y +1  
or, 6x - 2y = -20
or , 3x - y = -10
y= 3x + 10.-----------(1)
Now substituting back into (x+2)2 + (y+1)2=5,
(x+2)2 + (3x+10+1)2=5
or, (x+2)2 + (3x+11)2=5
or, x2 + 4x + 4 + 9x2 + 66x + 121 =5  
or, 10x2 + 70x + 120 = 0  
or, x2 + 7x + 12 = 0  
or, (x+4)(x+3) =0
So x = -4 or x=-3.
From (1), y =-2 or y=1.
So the two points are (-4,-2) and (-3,1).

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