Question

Focus of Parabola (y-2)² = 20(x+3) is

Answer 1

vertex -3,2
focus 2,2
standard parabola

Answer 2

STEP-BY-STEP EXPLANATION

First of all,we know that

(y-2)²=20(x+3),

∴ it's a standard rightwards opening parabola

now, substitute (y-2) as Y and (x+3) as X,

∴it becomes Y²=20X

∴focus⇒ 4a=20 ⇒ a=5; [Note: this is the focus of the parabola             if it had the origin as its vertex{old focus}]

∴co-ordinates of old focus ≡ (5,0)

we know from earlier that Y= y-2 and X= x+3

write it like this ⇒ x  =  X-3  

                              y  =  Y+2  [∴ vertex of the parabola is (-3,2)]

∴ new focus ≡ (5-3,0+2)

                      ≡ (2,2)  

HOPE THIS HELPS!!