Write the equation for a parabola with focus (0,-5/3) and directrix y=5/3.

x^2=20/3(y)

Step-by-step explanation:

Given:

focus of parabola=(0,-5/3)

directrix y=5/3

Standard form of parabola :

(x - h)^2 = 4p (y - k),

where focus is:

(h, k + p)

directrix  is :

y = k - p

Now equating the values we get

(0,-5/3)= (h,k+p)

h=0

k+p=-5/3

k=-5/3-p

Also

y=5/3 and y=k-p

i.e. k-p=5/3

Substituting k=-5/3-p in above we get:

-5/3-p-p=5/3

-2p=10/3

p=-5/3

Putting p=-5/3 in k-p=5/3 we get:

k-(-5/3)=5/3

k=5/3-5/3

k=0

Putting all the values in standard formula for parabola we get:

(x - (0))^2 = 4(-5/3) (y -(0))

x^2=-20/3(y) !

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step-by-step explanation: