If the chord of contact of the tangents to a parabola x^2=4ay, from an external point T(x1,y1) meets the directrix at R, prove that RT subtends a right angle at the focus.

Question

perl · Answer

mmmmm, you werent kidding around

mimi_x3 · Answer

Is this easy for you ? xD

perl · Answer

i will have to think about it

perl · Answer

the directrix is that line under the parabola

mimi_x3 · Answer

lols, you were thinking that its easy ? xD

mimi_x3 · Answer

Yup, y=-a

perl · Answer

what class is this  ?

mimi_x3 · Answer

I live in Australia, so its kinda different, there's only a maths class xD

perl · Answer

sorry wrong question, have you done calculus

mimi_x3 · Answer

Yes I have, how did you know ? xD

mimi_x3 · Answer

What grade are you in ?

perl · Answer

it will definitely help

perl · Answer

im a sophomore in college

mimi_x3 · Answer

Cool~ college, and you havent learnt that ?

perl · Answer

not specifically, but i bet i can do this

mimi_x3 · Answer

lols, then try hehe

perl · Answer

im trying to make a diagram, im not even sure i understand the question yet

perl · Answer

ok you have an external pt, and you want the tangent through it

mimi_x3 · Answer

Yeah, I don't really know where's the external point is, thats why im lost =/

perl · Answer

ok first thing is first. the chord of contact means something special

mimi_x3 · Answer

Something special ? What do you mean ?

perl · Answer

there is a picture of a chord of contacts http://www.nointrigue.com/docs/notes/maths/maths_parametrics.pdf

perl · Answer

well given an external point there are two tangents from that point to the parabola

perl · Answer

now where the tangents intersect the parabola, now draw a chord through those two points

perl · Answer

where the tangents meet the parabola, the two tangents

mimi_x3 · Answer

wow~ nice pdf file, its detailed on parametrics ty

mimi_x3 · Answer

But where is the external point ?

perl · Answer

anywhere

mimi_x3 · Answer

Can't it have to be specific

perl · Answer

in the pdf, the point is below the parabola

mimi_x3 · Answer

It can be but it doesn't make sense when it says RT subtends a right angle at the focus.

perl · Answer

like this

mimi_x3 · Answer

like this ?

perl · Answer

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