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Marina CMI [18]
3 years ago
6

A circle passes through (3,-1),(-2, 4), and (6,8)

Mathematics
1 answer:
Vaselesa [24]3 years ago
5 0

Answer:

D = -6, E = -8 , F = 0

Step-by-step explanation:

standard form = x^{2} + y^{2} + Dx + Ey + F = 0

now, when circle passes through (3,-1);

⇒ 3^{2} + (-1)^{2} + D(3) + E(-1) + F = 0

⇒ 3D - E + F + 10 = 0    ...............( equation 1)

when circle passes through (-2,4);

⇒ (-2)^{2} + 4^{2} + D(-2) + E(4)+ F = 0

⇒ -2D + 4E + F + 20 = 0    ...............( equation 2)

when circle passes through (6,8);

⇒ 6^{2} + 8^{2} + D(6) + E(8) + F = 0

⇒ 6D + 8E + F + 100= 0       ................( equation 3)

by solving these 3 equations , we get;

D = -6, E = -8, F = 0

hence,

standard form = x^{2} + y^{2} + Dx + Ey + F = 0

                        = x^{2} + y^{2} - 6x - 8y = 0

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