Conics Worksheet With Answers Page 8
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8Conics Lesson 6
Part III: General To Standard Form
Answers:
5.
2
2
4x + y - 8x + 4y - 9 = 0
1.
2
2
9x - 4y - 8y + 32 = 0
2
2
4x - 8x + y + 4y - 9 = 0
2
2
9x - 4(y + 2y) = -32
2
2
4(x - 2x)+(y + 4y) = 9
2
2
9x - 4(y + 2y + 1) = -32 - 4
2
2
4(x - 2x + 1)+(y + 4y + 4) = 9 + 4 + 4
2
2
9x - 4(y + 1) = -36
2
2
4(x - 1) +(y + 2) = 17
2
2
9x
4(y + 1)
-36
2
2
4(x - 1)
(y + 2)
-
=
+
= 1
36
36
36
17
17
2
2
x
(y + 1)
-
= -1
4
9
6.
2
2
9x - 4y - 40y - 136 = 0
2
2
9x - 4(y + 10y) = 136
2.
2
-2y - x + 20y - 47 = 0
2
2
9x - 4(y + 10y + 25) = 136 - 100
2
-2y + 20y = x + 47
2
2
9x
4(y + 5)
36
2
-2(y - 10y) = x + 47
-
=
36
36
36
2
-2(y - 10y + 25) = x + 47 - 50
2
2
x
(y + 5)
-
= 1
2
-2(y - 5) = x - 3
4
9
7.
3.
2
2
x + 6x + 8y + 33 = 0
y + 6y = 3x - 12
2
2
(y + 6y + 9) = 3x - 12 + 9
(x + 6x) = -8y - 33
2
2
(y +
3) = 3x - 3
(x + 6x + 9) = -8y - 33 + 9
2
2
(y + 3) = 3(x - 1)
(x + 3) = -8y - 24
1
2
(x + 3) = -8(y + 3)
2
x - 1= (y + 3)
3
1
2
y + 3 = - (x + 3)
8
2
2
25x - 9y - 72y - 100x - 269 = 0
4.
2
2
25x - 100x - 9y - 72y = 269
2
2
25(x - 4x) - 9(y + 8y) = 269
2
2
25(x - 4x + 4) - 9(y + 8y + 16) = 269 + 100 - 144
2
2
25(x - 2)
9(y + 4)
225
-
=
225
225
225
2
2
(x - 2)
(y + 4)
-
= 1
9
25
Pure Math 30: Explained!
112
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