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# Coordinates

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Find all points that are 13 units away from the point (-2,7) and that lie on the line x - 2y = 10. Give your answer as a list of points separated by semicolons, with the points ordered such that their x-coordinates are in increasing order. (So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

Oct 14, 2021

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Find all points that are 13 units away from the point (-2,7) and that lie on the line x - 2y = 10.

Hello Guest!

$$y=-\sqrt{13^2-(x+2)^2}+7\\ x - 2y = 10 \\-2y=10-x\\ y=\dfrac{x}{2}-5$$

$$\color{blue}-\sqrt{13^2-(x+2)^2}+7=\dfrac{x}{2}-5\\ -\sqrt{13^2-(x+2)^2}=\dfrac{x}{2}-12\\ +\sqrt{13^2-(x+2)^2}=12-\dfrac{x}{2}\\ 169-(x+2)^2=144-12x+\dfrac{x^2}{4}\\ 169-x^2-4x-4=144-12x+\dfrac{x^2}{4}$$

$$1.25x^2-8x-21=0$$

$$x = {8 \pm \sqrt{64+4\cdot 1.25\cdot 21} \over 2\cdot 1.25}$$

$$x=\dfrac{8\pm 13}{2.5}\\ y=\dfrac{x}{2}-5$$

$$\mathbb L=\{(-2,-6);(8.4,-0.8)\}$$

!

Oct 14, 2021
edited by asinus  Oct 14, 2021