#How do I do this?
dense topaz
ivory dragonBOT
dense topaz
I don't know where to start, anyone got any ideas?
simple plume
what is the equation of the quadratic?
also how do you know where A and B are on the parabola?
dense topaz
that information is not given in the question
simple plume
what that means is you can assume it
because if they don't give you that info that means it doesn't matter
so let's say the quadratic is just plain ol' y=x^2
actually y=4x^2 so that the "p" value is 1
the directrix will be y=-1
I mean 1/4*x^2
A and B are (2,1) and (-2,1) respectively
F is (0,1) A1 and B1 will be (2,-1) and (-2,-1) respectively
here is what it looks like
look at this diagram and you will notice that the slope of lines going from F to A1 and F to B1 have a slope of -1 and 1 respectively. Since they are opposite signs and recirpicol (1/1 = 1) they are perpendicular
now are you sure that the problem gave no other information about the equation of the parabola or where A and B are
dense topaz
yea the problem did not give any other information
simple plume
because if they didn't, that means that no matter the equation of the parabola and where you choose A and B to be on that parabola - it will always be 90 degrees
dense topaz
the angle is 90 for this case but how do we prove it for all the other cases
simple plume
did the problem ask to prove for all cases?
dense topaz
my teacher is going to yell at me
simple plume
so your teacher wants a general case?
dense topaz
yes he's gonna ask me how do i know this is for every case
simple plume
well the thing is, the problem kinda implies it works for every case
maybe the problem is asking to find the angle in terms of a, b and c and A and B where the equation of the parabola is ax^2+bx+c and A and B are the x coordinates of the points?
but then it shouldn't say "find the measure" it should say "solve for" or something like that
"find the measure" implies there is a numerical answer
dense topaz
yea i entered in 90 it says it is correct
simple plume
so do you still want to prove it?
cause that'd be a lot harder to prove it works for all parabolas
dense topaz
yes my teacher is going to say that its not sufficent to consider this one case
simple plume
is this for an online quiz thing?
dense topaz
no its homework we go over it in class today
simple plume
so how do you know you were correct
dense topaz
he asks us to enter the answer online
simple plume
I think it will be easier to start from vertex form (x-h)^2+k
for the general proof
what level of math are you currently taking?
dense topaz
this is homework on conic sections - parabolas
simple plume
wait it doesn't even work
well the best way to find an angle between 2 lines is something called a "vector dot product"
do you know what that is
dense topaz
no he is going to yell at me if i do that
dense topaz
AB needs to go through the focus
dense topaz
oh i proved it
i just proved that B1F and A1F are perpendicular bisectors
so 2 * <1 + 2 * <2 = 180 => <1 + <2 = 90
cuz by parabola definition BF = B1F so it is a isoceles triangle B1BF and similarly for A1AF