### Home > A2C > Chapter 11 > Lesson 11.3.3 > Problem11-156

11-156.

Find values of $A$, $B$, D, $E$, and $F i$n the equation $Ax^{2} + By^{2} + Dx + Ey + F = 0$ to create each of the following conic sections.

1. Line

Write an equation for a line then convert it into this general form.

$y = x$
$0x^{2} + 0y^{2} − x + y + 0 = 0$
$A = 0, B = 0, D = −1, E = 1, F = 0$

1. Point

See part (a).

What kind of equation defines a point?

$x^{2} + y^{2} = 0$
$x^{2} + y^{2} + 0x + 0y + 0 = 0$$A = 1, B = 1, D = 0, E = 0, F = 0$

1. Circle

See part (a).

1. Ellipse

See part (a).

1. Parabola

See part (a).

1. Hyperbola

See part (a).

$y^{2} − x^{2} = 1$
$−x^{2} + y^{2} = 0x + 0y −1 = 0$
$A = −1, B = 1, D = 0, E = 0, F = −1$