Conics Worksheet With Answers Page 3
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8Conics Lesson 6
Part II: Standard To General Form
Converting from Standard To General Form:
This is done by
multiplying both sides of the equation by the common denominator,
then simplifying:
5
2
Example 1: Convert
to general form:
y + 3 = (x + 3)
4
Multiply both sides by the
common denominator of 4:
Why General Form?
⎡
⎤
5
[
]
2
4 y + 3 = 4
(x + 3)
The general form of a conic is
⎢
⎥
⎣
⎦
4
of little use in Pure Math 30
since you require a special
⎡
⎤
5
conics program in your
2
4y + 12 = 4
(x + 3)
⎢
⎥
calculator to graph them.
⎣
⎦
4
However, in higher level
2
4y + 12 = 5(x + 3)
calculus courses the general
form will be used often
4y + 12 = 5(x + 3)(x + 3)
because it makes the algebra
(
)
much simpler.
2
4y + 12 = 5 x + 6x + 9
2
4y + 12 = 5x + 30x + 45
2
0 = 5x + 30x - 4y + 33
2
2
(x -10)
y
Example 2: Convert
+
=
1 to general form:
100
625
Multiply both sides by the common denominator of 62500:
⎡
⎤
2
2
(x - 10)
y
[ ]
62500
+
= 62500 1
⎢
⎥
⎣
100
625
⎦
2
2
625(x - 10) + 100y = 62500
2
2
625(x - 20x + 100)+ 100y = 62500
2
2
625x - 12500x + 62500 + 100y = 62500
2
2
625x + 100y - 12500x = 0
Pure Math 30: Explained!
107
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