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Circle Search (Posted on 2024-07-23)

The points of intersection of the curves with equations 21y = 5x² + 2x – 135 and 21y = (x – 5)(21x² + 26x - 225) all lie on a circle C. Find the center and radius of C.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 2

5x^2 + 2x – 135 = (x – 5)(21x^2 + 26x - 225)

(x - 5)(5x + 27) = (x – 5)(21x^2 + 26x - 225)

So (5,0) is one point of intersection

5x + 27 = 21x^2 + 26x - 225

21x^2 + 21x - 252 = 0

x^2 + x - 12 = 0

(x+4)(x-3) = 0

x values of intersection: {+5, -4, +3}

3 points of intersection (5,0) (-4,-3) (3,-4)

Center (0,0)

Radius 5

x^2 + y^2 = 25

https://www.desmos.com/calculator/ga9rktn32f

Posted by Larry on 2024-07-23 13:26:55

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