CPM Homework Help : A2C Problem 11-156

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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.

Line
Hint (a):
Write an equation for a line then convert it into this general form.
Example (a):
$y = x$
$0x^{2} + 0y^{2} − x + y + 0 = 0$
$A = 0, B = 0, D = −1, E = 1, F = 0$
Now create your own example.

Point
Hint (b):
See part (a).
More Help (b):
What kind of equation defines a point?
Example (b):
$x^{2} + y^{2} = 0$
$x^{2} + y^{2} + 0x + 0y + 0 = 0$ $A = 1, B = 1, D = 0, E = 0, F = 0$
Now create your own example.

Circle
Hint (c):
See part (a).

Ellipse
Hint (d):
See part (a).

Parabola
Hint (e):
See part (a).

Hyperbola
Hint (f):
See part (a).
Example (f):
$y^{2} − x^{2} = 1$
$−x^{2} + y^{2} = 0x + 0y −1 = 0$
$A = −1, B = 1, D = 0, E = 0, F = −1$
Now create your own example.

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