SOLUTION: how to write the equation of the line that passes through (1,1) and through the center of the circle (x-2)^2+ (y-4)^2=20

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Question 673487: how to write the equation of the line that passes through (1,1) and through the center of the circle (x-2)^2+ (y-4)^2=20
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the line that passes through (1,1) and through the center (h,k) of the circle %28x-2%29%5E2%2B+%28y-4%29%5E2=20
recall the standard form equation of a circle formula %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
where h and k are the x and y coordinates of the center of the circle
and the center of the circle will be second point the line that passes through
as you can see from %28x-2%29%5E2%2B+%28y-4%29%5E2=20, (h,k)=(2,4) and r=sqrt%2820%29=4.47
now we can find the equation of a line that passes through (1,1) and (2,4)

Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, 1) and (x2, y2) = (2, 4).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%284-1%29%2F%282-1%29+=+3.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 3%2A1+%2Bb+=+-2. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=1-3%2A1+=+-2.

y=(3)x + (-2)

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