Chords of a parabola (1 Viewer)

[vaaan]

So I was given a formula

Parametric Equation of the chord:
y = 1/2 (p+q)x - apq

I don't really get what to sub in etcetc. D: I'm extremely confused. Can someone explain this to me ? Using uhm the question below as an example.

Find the equation of the chord of the parabola joining the points with parameters 1 and -3 on x=2t, y=t^2

Thankyouu.

EDIT:// DWWW. I GET IT OHOHOHOH

 

[gurmies]

Here it's not necessary to use parameters in the final chord equation. When I do these, I eliminate it at the beginning. So you have:

x = 2t, y = t^2

When t = 1, x = 2, y = 1. Hence point is (2, 1)

When t = -3, x = -6, y = 9. Hence point is (-3, 9)

y - 1 = m (x - 2)

m = (1 - 9)/(2+3) = -8/5

y - 1 = -8(x-2)/5

5y - 5 = -8x + 16

8x + 5y - 21 = 0

 

[vaaan]

Yeaaahh. I did that, it's just I have a feeling that formula's a big part of this D: Cause in the next exercise I think it full asks us to like use it etcetec. Cause yeah I'm ont he first question, and it tells us to use the point gradient formula, but then it asks us to use y = 1/2 (p+q)x - apq. D:

 

[Drongoski]

So I was given a formula

Parametric Equation of the chord:
y = 1/2 (p+q)x - apq

I don't really get what to sub in etcetc. D: I'm extremely confused. Can someone explain this to me ? Using uhm the question below as an example.

Find the equation of the chord of the parabola joining the points with parameters 1 and -3 on x=2t, y=t^2

Thankyouu.

EDIT:// DWWW. I GET IT OHOHOHOH

Here: x = 2at and y = at^2

Therefore a = 1

Therefore eqn of chord is: y = (1/2)(1 - 3) x - 1 x 1 x (-3)

i.e. y = - x + 3

 

[vaaan]

Ahh tyty