Question

Write the general equation for the circle that passes through the points:

Answer 1

Answer:

x² + y² − 8x − 6y = 0

Step-by-step explanation:

The conic form of a circle is:

x² + y² + Dx + Ey + F = 0

Plugging in the three points:

(1)² + (7)² + D(1) + E(7) + F = 0

(8)² + (6)² + D(8) + E(6) + F = 0

(7)² + (-1)² + D(7) + E(-1) + F = 0

Simplifying:

50 + D + 7E + F = 0

100 + 8D + 6E + F = 0

50 + 7D − E + F = 0

Subtracting the first equation from the third:

(50 + 7D − E + F) − (50 + D + 7E + F) = 0

6D − 8E = 0

3D = 4E

Now if we subtract the third equation from the second:

(100 + 8D + 6E + F) − (50 + 7D − E + F) = 0

50 + D + 7E = 0

150 + 3D + 21E = 0

Substituting:

150 + 4E + 21E = 0

150 + 25E = 0

E = -6

Therefore, D = -8.

Plugging into any equation to find F:

50 + (-8) + 7(-6) + F = 0

F = 0

The equation of the circle is:

x² + y² − 8x − 6y = 0

Graph:

desmos.com/calculator/davg3d3lic