Circle Hyperbola

Hello ...
Sorry for the late post, but here's what we did on Friday.

First off, we went through the homework that were given on Thursday.

w + l + h = 80 cm
Length=10cm less than twice the sum of width and height and twice the width exceeds the height by 6 cm. Find the width, length and height of the box.

~We didn't go over the procedure on how to solve this problem, but the answers were:
h = 18cm, w = 12 cm, l = 50 cm

Then there was the question from the book (Ex. 25 #1) Letter "c" was done by Ramina on the white board. For those who didn't get to copy the procedure, here it is...

1. a) 3x-4y+5z=2
4x+5y-3z=-5
5x-3y+2z=-11

(3) 3x-4y+5z=2 (3)
(5) 4x+5y-3z=-5 (5)

9x-12y-15z=6
+ 20x+25y-15z=-25
ˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉ
29x+13y=-19


(2) 4x+5y-3z=-5 (2)
(3) 5x-3y+2z=-11 (3)

8x+10y-6z=-10
+ 15x-9y+6z=-33
ˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉ
23x+y=-43


29x+13y=-19
(13) 23x+y=-43 (13)

29x+13y=-19
+ 229x+13y=-559
ˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉˉ
-270x = 540
ˉˉˉˉˉˉ ˉˉˉˉˉ
-270 -270

x = -2


29x+13y=-19
29(-2)+13y=-19
-58+13y=-19
13y=58-19
13y=39
ˉˉˉ ˉˉˉ
13 13

y = 3


3x-4y+5z=2
(3)(-2)-4(3)+5z=2
-6-12+5z=2
-18+5z=2
5z=18+2
5z = 20
ˉˉˉ ˉˉˉ
5 5

z = 4


After this, we talked about a little something new called Circle Hyperbola.
It looks like this ...



A Circle Hyperbola can only have 0, 1, or 2 intercepts and no more than that. We can find the intercept by putting the equation on our calculator OR solve it algebraically. We did some examples as a practice on finding the intercepts of Circle Hyperbola.

► y=x-1
y=x²-6x+9

x-1=x²-6x+9
-10=x²-7x
x²-7x+10=0
(x-5) (x-2)
x=5 x=2
y=4 y=1

another example was...

►x²-y²=5
xy+6=0

y²=x²-5 → y= √x²-5 (#1)

y=-6/x (#2)

-6/x=√x²-5
(-6/x)² = (√x²-5)²
36/x² = x²-5
x^4-5x²=36 (substitute x^4 to u=x²)
u²-5u-36=0
(u-9) (u=4)
u=9, -4
x²=9, -4
x=±3
x=3 , y=-2
x=-3 , y=2

After doing these examples, there were homework that were assigned for us to do. Exercise 26 (# 1-5) Also, don't forget to hand in your bonus mark homework sheets before Dr. Eviatar leaves!

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Next Scribe ... Jamie