Answer:
D= -16
E= 0
F= 0
Step-by-step explanation:
The given equation is [tex]x^{2} + y^{2} + Dx + Ey + F = 0[/tex]
It is also given that the circle passes through (0,0) (16,0) and (8,8).
Inserting (0,0) in the equation, it gives
[tex]0 + 0 + 0 + 0 + F = 0[/tex]
This gives F = 0 .
Now inserting (16,0) , it gives
[tex]16^{2} + 0^{2} + D(16) + E(0) + 0 = 0[/tex]
[tex]D(16) = -256[/tex]
[tex]D = \frac{-256}{16}[/tex]
D = -16
Now inserting (8,8) , it gives
[tex]8^{2} + 8^{2} + (-16)(8) + (E)(8) + 0 = 0[/tex]
[tex]-16 + E = -16[/tex]
E = 0
Thus the equation of circle is
[tex]x^{2} + y^{2} + (-16)x = 0[/tex]
We can draw the following graph and thus verify that points (0,0) (8,8) and (16,0) lie on graph.
