give the focus directrix and vertex of the following parabolas: a) (x+3)^2=4y b)

Question

give the focus directrix and vertex of the following parabolas: a) (x+3)^2=4y b) x^2=4(y-2) c) ( x-5)^2=-3(x+2) d) x=y^2-3y-1
Please show all work and explain. Thank you!

give the focus directrix and vertex of the following parabolas: a) (x+3)^2=4y b) x^2=4(y-2) c) ( x-5)^2=-3(x+2) d) x=y^2-3y-1
Please show all work and explain. Thank you!

give the focus directrix and vertex of the following parabolas: a) (x+3)^2=4y b) x^2=4(y-2) c) ( x-5)^2=-3(x+2) d) x=y^2-3y-1
Please show all work and explain. Thank you!

Explanation / Answer

a) (x+3)^2=4y

4a =4 ,

a=1

vertex=>(-3,0)

focus =>(-3,1)

directrix=> y =-1

b) x^2=4(y-2)

4a =4

a=1

vertex=>(0,2)

focus =>(0,3)

directrix=>y=1

c) ( x-5)^2=-3(x+2)

not a parabola

d) x=y^2-3y-1

x+1=y^2 -3y

x+1+(9/4)=y^2 -3y +(9/4)

(x+(13/4))=(y -(3/2))2

4a =1

a =1/4

vertex:(-13/4 ,3/2)

focus :(-13/4 +1/4 ,3/2)=(-3,3/2)

directrix:x =-13/4 -1/4

x =-7/2

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