4. A conic section in mathematics is a curve obtained from the intersection of a cone surface and a plane. Conics are related mathematically since the equations used to describe each figure are similar. The general form of the equation for each is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 They differ because of the restrictions placed on the coefficients in the table below; Circle A = C and B = 0 Ellipse A C but have the same sign. B = 0 Parabola A or C = 0. B = 0 Hyperbola A and C have different signs. B = 0 For the circle A and C must be equal and B must equal 0. For the ellipse, A and C cannot be equal but must have the same sign. B must equal 0. The general equation above is not very useful for determining information about the position of the figure on the coordinate axis system. The equations must be modified to standard form:

	Circle	Ellipse	Parabola	Hyperbola
Equation (horiz. vertex):	x2 + y2 = r2	x2 / a2 + y2 / b2 = 1	4px = y2	x2 / a2 - y2 / b2 = 1

Write a Java program given the general form of the equation, determine if it is a circle, an ellipse, a hyperbola or a parabola and give other information about the figure. Input from the keyboard six integers representing the coefficients of the general equation. Output the type figure the equation produces to the screen as follows: If it is a circle, print the location of its center in ordered pair format (x,y) and its radius. If it is an ellipse, print the location of its center in ordered pair format (x,y) and the length of its major axis. If it is a hyperbola, print its center in ordered pair format (x,y) and the equation of the principal axis. If it is a parabola, print its vertex in ordered pair format (x,y) and the equation of the axis of symmetry. Finally, ask the user if he/she wishes to run the program again. Refer to the sample output below.