Conics Worksheet With Answers Page 6
ADVERTISEMENT
1
2
3
4
5
6
7
8Conics Lesson 6
Part III: General To Standard Form
Converting from General To Standard Form:
This is done by
completing the square:
2
2
Example 1: Convert x
+ 3y
+ 10x - 30y + 91 = 0 to general form.
Step 1:
Group terms with x, group terms with y, and take the constant to the other side.
2
2
x
+ 10x + 3y
- 30y = -91
Step 2:
Put brackets around the x-terms, and put brackets around the y-terms, leaving a space.
2
2
(x
+ 10x
) + (3y
- 30y
) = -91
Step 3:
Make sure the squared terms have a coefficient of 1. If they don’t, factor that number out.
2
2
(x
+ 10x
) + 3(y
- 10y
) = -91
Step 4:
Divide the x-coefficient by 2, square the result, and add inside the bracket. Repeat for y.
2
2
(x
+ 10x + 25) + 3(y
- 10y + 25) = -91
Step 5:
Whatever you do to one side, you must do to the other! On the left, you have now added
25 in the x-brackets, and 75 in the y-brackets (multiplying the 3 through the brackets).
Add 25 + 75 to the other side to keep things balanced.
2
2
(x
+ 10x + 25) + 3(y
- 10y + 25) = -91 + 25 + 75
Step 6:
Factor the expressions.
2
2
(x + 5)
+ 3(y — 5)
= 9
Step 7:
Divide both sides by 9 so the equation equals 1, which is required for standard form:
2
2
(x + 5)
3(y - 5)
9
+
=
9
9
9
2
2
(x + 5)
(y - 5)
+
= 1
9
3
2
Example 2: Convert 3x
+ 12x - 4y - 12 = 0 to general form.
2
Step 1:
Group terms with x. Since there is no y
, take both the 4y & 12 to the other side.
2
3x
+12x = 4y + 12
Step 2:
Put brackets around the x-terms, leaving a space.
2
(3x
+12x
) = 4y + 12
Step 3:
Make sure the squared terms have a coefficient of 1. If they don’t, factor that number out.
2
3(x
+4x
) = 4y + 12
Step 4:
Divide the x-coefficient by 2, square the result and add inside the bracket.
2
3(x
+4x + 4) = 4y + 12 + 12
Step 5:
Whatever you do to one side, you must do to the other! On the left, you
have added 12 (multiplying the 3 into the brackets), so add 12 to the other side too.
2
3(x
+4x + 4) = 4y + 12 + 12
Step 6:
Factor and simplify the expressions.
If you are ever asked to graph a conic
2
3(x + 2)
= 4y + 24
presented in general form, you must
Step 7:
Take this to parabola standard form.
first convert it to standard form.
2
Once converted, you can use rules
3(x + 2)
4(y + 6)
=
from previous lessons to draw the
4
4
graph.
3
2
y + 6 = (x + 2)
4
Pure Math 30: Explained!
110
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education