Question

Which equation represents a parabola opening to the left with a vertex at the origin and a focus at (-7, 0)?

a. x=1/28 y^2
b. x= - 1/28 y^2
c. y= 1/20 x^s
d. y= - 1/20 x^s​

Answer 1

b. x=1/28 y^2

Explanation:

the standard equation,

`y^(2) = 4ax` ---(1) , when opening towards left or right

focus at (a , 0)

`x^(2) = 4ay` ---(2) , when opening towards top or bottom

focus at (0, a)

if a is negative parabola will open toward negative axes ( down or left) and vice versa.

re- arranging option b. we get

`y^(2) =28 x\\y^(2) = 4 X (-7 x)` -----(3)

therefore, a = -7

(3) is similar to (1)

So it is facing left with focus at (-7,0)