Question

For parabola (y-3)²=8(x-1)

1.Vertex
2.focus
3.Equation of directrix​

Answer 1

$\huge{\underline{\sf{\red{Answer}}}}$

Given:

(y-3)²=8(x-1)

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Solution:

By the parabola we get

(y-3)²=8(x-1)

$\implies 4a=8 \\ \implies \boxed{a=2}$

1.Vertex

Vertex=(0,0)

$\implies x-1=0 , y-3=0 \\ \\ \implies x=1,y=3 \\ \\ \leadsto{\boxed{V(1,3)}}$

2.Focus

Focus=(a,0)

$\implies x-1=a , y-3=0 \\ \\ \implies x-1=2 , y=3 \implies x=1 ,y=3 \\ \\ \leadsto \boxed{s(1,3)}$

3.Equation of directrix

x=-a

$\implies x-1=-2 \\ \\ \implies x=-1 \\ \\ \leadsto \boxed{x+1=0}$

Answer 2

$\huge{\tt{\green{Given}}}$

(y-3)²=8(x-1)

★Solution★

By the parabola

$(y-\beta)^2=4a(x-\alpha)$

we get that

$\implies 4a=8 \\ \implies a=\dfrac{8}{4} \\ \implies \huge{a=2}$

1.Vertex

we know,

→Vertex=(0,0)

X=0 , Y= 0

Here X = x-1 and Y=y-3

$\implies x-1=0 , y-3=0 \\ \\ \implies x=1,y=3 \\ \\ \leadsto{\boxed{V(1,3)}}$

2.Focus

Focus=(a,0)

X=a ,Y=0

$\implies x-1=a , y-3=0 \\ \\ \implies x-1=2 , y=3 \implies x=1 ,y=3 \\ \\ \\leadsto \boxed{s(1,3)}$

3.Equation of directrix

x=-a

$\implies x-1=-2 \\ \\ \implies x=-1 \\ \\ \leadsto{\boxed{x+1=0}}$