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If the focus of a parabola is (0,-3) and...

If the focus of a parabola is `(0,-3)` and its directrix is `y=3,` then its equation is

A

`x^(2)=-12y`

B

`x^(2)=12y`

C

`y^(2)=-12x`

D

`y^(2)=12x`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that, focus of parabola at `F (0,-3)` and equation of directrix is `y=3`
Let any point on the parabola is P (x,y).
Then, `PF`=`abs(y-3)`
`rArr sqrt((x-0)^(2)+(y-3)^(2))=abs(y-3)`
`rArrx^(2)+y^(2)+6y+9=y^(2)-6y+9`
`rArrx^(2)+12y=0`
`rArrx^(2)=-12y`
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Knowledge Check

  • If the focus of a parabola is at (0,-3) and its directrix is y = 3, then its equation is

    A
    `x^(2)=-12y`
    B
    `x^(2)=12y`
    C
    `y^(2)=-12x`
    D
    `y^(2)=112x`

  • If the focus of parabola is at (0,-2) and its directrix is y = 3 , then its equation is

    A
    `x^2=-12y`
    B
    `x^2=12y`
    C
    `y^2=-12y`
    D
    `y^2=12x`

  • If the focus of parabola is at (0, - 3) and its directrix is v = 3, then its equation is

    A
    `x^(2)=-12y`
    B
    `x^(2)=12y`
    C
    `y^(2)=-12y`
    D
    `y^(2)=12x`

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