SOLUTION: The centre of a circle is (2x-1, 3x + 1). Find x if the circle passes through (-3,-1) and the length of its diameter is 20 unit.

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Question 895413: The centre of a circle is (2x-1, 3x + 1). Find x if the circle passes through (-3,-1) and the length of its diameter is 20 unit.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The distance from (2x-1, 3x + 1) to (-3,-1) is 20 units.
Use Distance Formula, and ... solve for x.

Do you still need help?

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The centre of a circle is (2x-1, 3x + 1). Find x if the circle passes through (-3,-1) and the length of its diameter is 20 unit.


Center-radius equation of a circle: %28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2, with:

(x, y) being:  (-+3, -+1)

(h, k) being:  (2x+-+1, 3x+%2B+1), and

r, or radius being: 10

%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2 becomes: %28-+3+-+%282x+-+1%29%29%5E2+%2B+%28-+1+-+%283x+%2B+1%29%29%5E2+=+10%5E2____Substituting values into center-radius equation of a circle

%28-+3+-+2x+%2B+1%29%5E2+%2B+%28-+1+-+3x+-+1%29%5E2+=+10%5E2

%28-+2x+-+2%29%5E2+%2B+%28-+3x+-+2%29%5E2+=+10%5E2

4x%5E2+%2B+8x+%2B+4+%2B+9x%5E2+%2B+12x+%2B+4+=+100

4x%5E2+%2B+9x%5E2+%2B+8x+%2B+12x+%2B+4+%2B+4+-+100+=+0

13x%5E2+%2B+20x+-+92+=+0

13x%5E2+%2B+46x+-+26x+-+92+=+0

x%2813x+%2B+46%29+-+2%2813x+%2B+46%29+=+0

%28x+-+2%29%2813x+%2B+46%29+=+0

highlight_green%28highlight_green%28x+=+2%29%29         OR        highlight_green%28highlight_green%28x+=+-+46%2F13%29%29

You can do the check!! 



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