Question

HELP<3 Medalllllllls
Find the equation for the parabola with vertex (0, 0) and directrix x = 4.

Answer 1

*breathes*


Rather than fiddling with standard forms it's best to go back to basic focus-directrix definition.

i.e. “dist from focus" = "perp dist from directrix”

Let P(x,y) be any point on parabola then

dist from focus (0,0) is √(x²+y²)

perp dist from directrix x+y−4=0 is |x+y−4| / √(1²+1²) = |x+y−4| / √2

(this is a standard result, |...| is necessary because dist may come out ±)

∴ parabola is √(x²+y²) = |x+y−4| / √2

The √ and |...| can be eliminated by squaring both sides

x²+y² = (x+y−4)² / 2

2(x²+y²) = x²+y²+16+2xy−8x−8y

x²−2xy+y²+8x+8y−16 = 0

Answer 2

Wow, thanks chica but the 4 answer choices are A. x = (1/16)y2
B. y = (1/16)x2
C. x = (–1/16)y2
D. y = (–1/16)x2

Answer 3

You are amazingly educated though. You're gonna get far in life :3

Answer 4

B. y = (1/16)x2

I'm Asian. LOL

Answer 5

You're gorgeous, smart, and not american. What everyone wishes they were like.

Answer 6

Lol. Thanks ^^