Question

Medal for Answer

Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.

f(x) = one fourthx2 − x + 4

f(x) = −one fourthx2 − x + 4

f(x) = one fourthx2 − x + 5

f(x) = −one fourthx2 − x + 5

Answer 1

@dan815 @dsood15 @desiswag @DoShKa_SyRiA

Answer 2

@lupita1995 @love_jessika15

Answer 3

@Ashleyisakitty

Answer 4

@KlOwNlOvE

Answer 5

@robtobey

Answer 6

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1.

f(x) = −one twelfth (x − 5)2 + 2

f(x) = one twelfth (x − 5)2 + 2

f(x) = −one twelfth (x + 5)2 + 2

f(x) = one twelfth (x + 5)2 + 2

Answer 7

when focus and directrix are given use the deinition of the parabola or locus method..
let (x,y) be the point on the reqd parabola
then distance of (x,y) from (-2,4) is sqrt ( (x+2)^2+(y-4)^2 )
and distance of (x,y) from y=6 is
(y-6) units
so by definition of parabola
we have
sqrt ( (x+2)^2+(y-4)^2 ) = (y-6)
squaring both sides
we have
(x+2)^2+(y-4)^2 =(y-6)^2 and now just simplify