Question

HELP ME!!! find the length of the chord common to the parabolas y^2 = 2x + 4y + 6 and y^2 = 3x + 3y +1

Answer 1

I drew your graphs in desmos.com and they don't seem to have a common chord, unless I misunderstand your question?

Answer 2

it is really written on the book. hehe

Answer 3

Don't mind me, I'm confused lol.

Answer 4

you may isolate x in both equations and find intersect points with equating x's in terms of y

Answer 5

find the 2 intersection points of 2 parabolas, then use distance formula to get length of chord

Answer 6

thank you :)

Answer 7

actually the 2 parabola's intersect

the easy way to find the equation of the chord if to equate the 2 equations are they are both equal to y^2

then simplify and you'll get the equation of the chord

Answer 8

you don't need to find points of intersection... or anything else... is a difficult problem to understand by simple to get the solution

Answer 9

can you show it to me step by step?

Answer 10

ok so the equations are

\[y^2 = 2x + 4y + 6... and..... y^2 = 3x + 3y + 1\]

so you end up with

\[2x + 4y + 6 = 3x + 3y + 1\]

its that simple

Answer 11

\[10\sqrt{2}\]

Answer 12

is the answer

Answer 13

here is the graph

Answer 14

ops I read equation rather than length...sorry about that

Answer 15

so just find where the chord intersects... and you'll get the 2 points for the distance

Answer 16

@zith how did you get that 10 square root blabla? :)

Answer 17

so you are looking at

\[(x -5)^2 = 3x + 3(x -5) + 1\]

just work on that...

Answer 18

@campbell_st how?

Answer 19

Simplify campbell's last equation into the form
y = mx + b
then use that equation and the equation of one of the parabolas to solve for x and y.

You should end up with 2 points (x, y).

Use those points and pythagoras to calculate the length.

Answer 20

\[x^2 -10x + 25 = 3x + 3x -15 + 1... or .... x^2 -16x + 39 = 0\]

which factors to

(x - 3)(x - 13) = 0

so the x values are x = 3 and x = 13

so the y values are y = -2 and y = 8

so the points are (3, -2) and (13, 8)

find the distance between them

Answer 21

so i have already told u about distance formula it is

Answer 22

Thank you so much @Mandre :)