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Like the circle and the ellipse, the standard equation of a hyperbola can be expanded into an equation of the form Ax2 + By2 + Cx + Dy + F = 0

Let's look at a few examples to see how this is done.

EXAMPLE 1:
The equation -(x + 4)2/ 4 + (y - 2)2/ 16 = 1 describes a hyperbola is centred at (-4, 2) and opens up and down. Let's write this equation in the form Ax2 + By2 + Cx + Dy + F = 0.
Equation to expand:	-(x + 4)2/ 4 + (y - 2)2/ 16 = 1
Multiply each term by the lowest common multiple of the two denominators, 16:	-16(x + 4)2/ 4 + 16(y - 2)2/ 16 = 16
Simplify the fractions:	-4(x + 4)2 + (y - 2)2 = 16
Expand the squared terms:	-4(x2 + 8x + 16) + (y2 - 4y + 4) = 16
Multiply:	-4x2 -32x - 64 + y2 - 4y + 4 = 16
Write in the form Ax2 + By2 + Cx + Dy + F = 0:	-4x2 + y2 - 32x - 4y - 76 = 0

EXAMPLE 2:
The standard equation x2/ 8 - y2/ 6 = 1 describes a hyperbola that is centred at the origin and opens left and right. Let's write this equation into the form Ax2 + By2 + Cx + Dy + F = 0.
Equation to expand:	x2/ 8 - y2/ 6 = 1
Multiply each term by the lowest common multiple of the two denominators, 24:	24x2/ 8 - 24y2/ 6 = 24
Simplify the fractions:	3x2 - 4y2 = 24
Write in the form Ax2 + By2 + Cx + Dy + F = 0:	3x2 - 4y2 -24 = 0

The following are exercises for you to practice writing the standard equation of an hyperbola as a general equation.