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Forum URL: http://www.cut-the-knot.org/cgi-bin/dcforum/forumctk.cgi
Forum Name: High school
Topic ID: 195
Message ID: 2
#2, RE: Parabolas ...
Posted by leiyou on Sep-03-02 at 11:43 PM
In response to message #1

>>4c(ax by) 2abxy-a^2*y^2-b^2*x^2
>>---------------------------------------------------------- =
>>0
>> a^2 b^2

> This is correct, except you may remove the positive denominator.

how is it done though?

> But what are a, b, c, and x?

k, err i assumed that the directrix is x+y+1=0

then in the above formula A=1,B=1,C=1

so the the above formula can be rewritten as

4(x+y)+2xy-y^2-x^2=0

i.e

y^2-4y-2xy+x^2-4x=0

this can be seem as a new quadratic when we subst in x

y^2-(4+2x)y+(x^2-4x)=0

where b=-(4+2x)
c=(x^2-4x)

so the formula is correct right? (then it must be the way i attempted to plot it. thank you