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(Solved): If A,B,C, and D are real numbers, then the set of points in the plane satisfying the equation: A(x^ ...
If
A,B,C, and
Dare real numbers, then the set of points in the plane satisfying the equation:
A(x^(2)+y^(2))+Bx+Cy+D=0is called a generalized circle. (a) Show that if
A=0, then the generalized circle is a line. (b) Suppose that
A!=0and let
\Delta =B^(2)+C^(2)-4AD. Complete the square in
xand
yto show that a generalized circle is a circle centered at
((-B)/(2A),(-C)/(2A))with radius
(\sqrt(\Delta ))/(2A)provided
\Delta >0. (If
\Delta <0, the generalized circle is often called an imaginary circle.)
