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If the focus of the parabola x^2-k y+3=0...

If the focus of the parabola `x^2-k y+3=0` is (0,2), then a values of `k` is (are)

A

4

B

6

C

3

D

2

Text Solution

Verified by Experts

The correct Answer is:
B, D
2,4 The given parabola is
`x^(2)-ky+3=0`
`orx^(2)=k(y-(3)/(k))`
Let `x=Y,y-(3)/(k)=X`
Then the parabola is
`Y^(2)=kX`
whose focus is (0,k/4).
Therefore, the focus of
`x^(2)=k(y-(3)/(k))` is
`(0,(3)/(k)+(k)/(4))-=(0,2)`
`:.(3)/(k)+(k)/(4)=2`
`or12+k^(2)=8k`
`ork^(2)-8k+12=0`
`or(k-6)(k-2)=0`
`ork=2,6`
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Knowledge Check

  • The focus of the parabola y ^(2) -x -2y+2=0 is at-

    A
    `((1)/(4), 0)`
    B
    `((5)/(4) , 1)`
    C
    `(1,2)`
    D
    `(1,(5)/(4))`

  • x - 1 = 0 is the equation of directrix of the parabola y^(2) - kx + 8 = 0 . Then the value of k is _

    A
    `1/8`
    B
    `8`
    C
    `4`
    D
    `1/4`

  • The coordinates of focus of the parabola y^(2) =- 5x are _

    A
    `(-(5)/(4),0)`
    B
    `((5)/(4),0)`
    C
    `((4)/(5),0)`
    D
    `(-(4)/(5),0)`

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