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If ( 0,4) and (0,2) are the vertex and f...

If ( 0,4) and (0,2) are the vertex and focus of a parabola then its equation is

A

`x^(2) + 8y =32`

B

`y^(2) + 8x = 32`

C

`x^(2)-8y = 32`

D

`y^(2) - 8x = 32`

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The correct Answer is:
A
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The axis of a parabola is along the line y=x and the distance of its vertex and focus from the origin are sqrt(2) and 2sqrt(2) , respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is (x+y)^2=(x-y-2) (x-y)^2=(x+y-2) (x-y)^2=4(x+y-2) (x-y)^2=8(x+y-2)

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Knowledge Check

  • If (0,6) and (0,3) are respectively the vertex and focus of a parabola then its equation is

    A
    `x^2 + 12y = 72`
    B
    `x^2 - 12y = 72`
    C
    `y^2 - 12x = 72`
    D
    `y^2 + 12x = 72`

  • The vertex of the parabola y^2 + 4x = 0 is

    A
    `(4,0)`
    B
    `(-4,0)`
    C
    `(-1,0)`
    D
    `(0,0)`

  • The vertex of the parabola y^2 = 4x + 4y is

    A
    `(1,-2)`
    B
    `(-1,2)`
    C
    `(2,1)`
    D
    `(-2, 1)`

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    Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus of the parabola. The length of latus rectum of the parabola is

    A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then the locus of the focus of the parabola is :

    If the centre, vertex and focus of a hyperbola be (0,0), (4,0) and (6,0) respectively, then the equation of the hyperbola is

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    An equilateral triangle is inscribed in the parabola y^(2) = 4ax whose vertex is at the vertex of the parabola. Find the length of its side.

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