Question

The curve y^2= 12x intersects the line 3y = 4x+ 6 at two points. Find the distance between the two
points.
Thanks for any help in advance.

Answer 1

elimination and subtitution method is work

Answer 2

from the equation of line :
3y = 4x+ 6
y = (4x+6)/3 ... (1)

subtitute the value of y above into the equation y^2 = 12x, we get
((4x+6)/3)^2 = 12x
(16x^2 + 48x + 36)/9 = 12x
16x^2 + 48x + 36 = 9 * 12x
16x^2 + 48x + 36 = 108x
16x^2 + 48x + 36 - 108x = 0
16x^2 -60x + 36 = 0
divide by 4 on both sides, simplied be
4x^2 - 15x + 9 = 0
now, can you find the solution for x from the equ above?

Answer 3

(4x-3)(x-3)
x=3/4, 3
Coordinates = (3/4, 3) and (3, 6)
Distance=
Distance = SquareRoot(2.25^2+3^2)=3.75
Thanks for your help RadEn!

Answer 4

waw, you got it... im not yet get it, hehe..
you're welcome