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The point (8,4) lies inside the parabola...

The point (8,4) lies inside the parabola `y^(2) = 4ax ` If _

A

`alt(1)/(2)`

B

`a le (1)/(2)`

C

`a gt (1)/(2)`

D

`a ge (1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If the points of intersection of the parabola y^(2) = 4ax and the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 are (x_(1), y_(1)) ,(x_(2) ,y_(2)) ,(x_(3), y_(3)) and (x_(4), y_(4)) respectively , then _

    A
    `y _(1) + y_(2) + y_(3)+y_(4) = 0 `
    B
    `sqrt(x)_(1)+sqrt(x)_(2)+sqrt(x)_(3)+sqrt(x)_(4) = 0 `
    C
    `y _(1) - y_(2) + y_(3) - y _(4) = 0 `
    D
    `y _(1) - y_(2) - y_(3) + y _(4) = 0 `

  • If a ne 0 and the line 2 bx +3 cy +4d=0 passes through the points of intersection of the parabolas y ^(2) =4ax and x^(2) =4 ay , then-

    A
    `d ^(2) +(2b -3c) ^(2)=0`
    B
    `d^(2) +(3b +2c)^(2) =0`
    C
    `d ^(2) +(3b+2c )^(2) =0`
    D
    `d^(2) +(2b +3c)^(2) =0`

  • y_(1) and y_(2) and y_(3) are the ordinates of three points on the parabola y ^(2) = 4ax, then the area of the triangle formed by the points is-

    A
    `|(1)/(4a) (y_(1)-y_(2)) (y_(2)-y_(3)) (y_(3) -y_(1))|`
    B
    `|(1)/(16a) (y_(1)-y_(2)) (y_(2)-y_(3)) (y_(3) -y_(1))|`
    C
    `|(1)/(2a) (y_(1)-y_(2)) (y_(2)-y_(3)) (y_(3) -y_(1))|`
    D
    `|(1)/(8a) (y_(1)-y_(2)) (y_(2)-y_(3)) (y_(3) -y_(1))|`

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