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oksian1 [2.3K]
2 years ago
12

Help 30 point question!

Mathematics
1 answer:
Gennadij [26K]2 years ago
4 0

You're given 3 points (<em>x</em>, <em>y</em>) on the circle with equation

<em>x</em> ² + <em>y</em> ² + <em>Dx</em> + <em>Ey</em> + <em>F</em> = 0

and you have to use these known points on set up 3 equations involving <em>D</em>, <em>E</em>, and <em>F</em>.

For the point (3, -1), this means when <em>x</em> = 3, <em>y</em> = -1, so

3² + (-1)² + 3<em>D</em> - <em>E</em> + <em>F</em> = 0

→   3<em>D</em> + (-1)<em>E</em> + 1<em>F</em> = -10

The next point (-2, 4) gives

(-2)² + 4² - 2<em>D</em> + 4<em>E</em> + <em>F</em> = 0

→   (-2)<em>D</em> + 4<em>E</em> + 1<em>F</em> = -20

And from the last point (6, 8),

6² + 8² + 6<em>D</em> + 8<em>E</em> + <em>F</em> = 0

→   6<em>D</em> + 8<em>E</em> + 1<em>F</em> = -100

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