Mr Max expanded our knowledge on conics. The central idea of today's lesson is that we can change general form conics into standard form conics.
Conversion between general form conic and standard conics.
Ax^2 + Bxy + Cx^2 + Dx + Ey + F = 0
Remember how to complete the square?
Take: x^2 + 4x + 4
We can take a square and
(x+2)(x+2)
(x+2)^2
or:
How do we find x? Well, take b/2, and square the result. sqroot(3/2)
If we try to enter (X^2 + y^2 + 6x - 8y) = 11 into graphimatica directly, it fails to map the equation because it cannot parse the data. So, we use this form after we complete the square
(X^2 + y^2 + 6x - 8y) = 11
(x^2+6x+9)(y^2-8y+16) = 11 + 9 + 16
(x+3)^2 + (y - 4)^2 = 36
Using the general form:
(x-h)^2+(y-k)^2= r^2
(h,k) = center; r = radius
we enter (x+3)^2+(y-4)^2= 36
and get:
c)4x^2 - y^2 - 8x - 4y - 16 = 0
4x^2-8x -y-4y = 16 + 4 -4
4(x^2-2x+1) -1(y^2+4y+4) = 16 + 4 - 4
(4(x-1)^2 / 16) - ((y+2)^2 / 16) = (16 /16)
(x-1)^2/(2^2) - (y+2)^2/(4^2) = 1
(x-h)^2 / a^2 - (y+2)^2/b^2 = 1
The final is only ~27 days away. I'm going to start studying today! Yes, that sounds crazy, but the exam is difficult, and this class can be interpreted as being preparation for the exam.
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