One thing this week that i really picked up pretty well was Conics. So I'll go straight into that. The steps to find the intersection of a line and a circle are: solve the linear equation for y, next substitute in circle equation, after this you solve for x, and last you plug x value in to get y value **If your x value is imaginary, then there is no point of intersection.
So for example, say you have:
x^2+y^2+12y+16x-5=0
First you rewrite the problem in order with x's in front and y's in back, or vice versa, and you would get this:
x^2+16x__+y^2+12y__=5
Next you would fill in the blanks with the number that belongs, for this you divide the x and y by 2 and then square it. For this problem you would use 16x and 12y, and you would get 64 and 36. So the answer would be:
x^2+16x+64+y^2+12y+36=5
After this you add the new numbers to the other side of the problem and you would get this:
x^2+16x+64+y^2+12y+36=5+64+36
or
x^2+16x+64+y^2+12y+36=105
Then you factor out the x's and y's and you should get this:
(x+8)^2+(y+6)^2=105
In the end you would get this:
Center=(-8,-6) Radius=square root of 105
This week I did have one little problem with Hyperbolas. I don't understand how we've been getting the foci when we sketch the problem. So if anyone can help me with that little problem I would be very grateful.
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to find the foci use: c^2 = a^2 + b^2
ReplyDeleteexample: x^2/16 - y^2/25
c^2 = a^2 + b^2
= 16 + 25
= 41
= √41
Foci: (√41, 0) , (-√41, 0)
see simple...
This is going to be short and sweet because its really simple so it wont take much to explain.
ReplyDeleteOn your 6th step when doing hyperbolas you solve for c. The + or - answer that you get from solving for c is your points on your graph for your foci.
Ex: c^2=36+9
c^2=45
c= +or- the squareroot of 45.
your foci points would be (squareroot of 45,0)and (-squareroot of 45,0)
which on your graph would be 6.7!!!
Goodluck on your exam! i hope this helped :)
When finding the focus, you use the formula
ReplyDeletec^2=x-denominator+y-denominator
so if you have an equation
x^2/4+y^2=1
your focus would be
(6,0) (-6,0)
**sould be**
ReplyDelete(squareroot 6,0)(-squareroot 6,0)