Question

I need help with 6-8

Answer 1

6. y² = 169x

7. y² = 12x

8.
`y^(2) = (1)/(2)x`

Explanation:

The equation of a quadratic function in vertex form is given by

(y - α)² = 4a(x - β)

Where, (α,β) is the vertex of the function and a is the distance from vertex to its focus.

6. Here, (α,β) ≡ (0,0) and a point on the equation is (1,13)

So, the equation will be y² = 4ax

⇒ 13² = 4a(1)

⇒ 4a = 169

Therefore, the original equation will be y² = 169x (Answer)

7. Here also the vertex is (0,0) and a point on the equation is (3,-6),

So, (-6)² = 4a(3)

⇒ 4a = 12

So, the equation is y² = 12x (Answer)

8. Here also the vertex is (0,0) and a point on the equation is (
`(1)/(2),(1)/(2)`),

So,
`((1)/(2))^(2) = 4a((1)/(2))`

⇒
`4a = (1)/(2)`

So, the equation is
`y^(2) = (1)/(2)x` (Answer)