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STATEMENT-1 : The area of equilateral tr...

STATEMENT-1 : The area of equilateral triangle inscribed in the circle `x^(2) + y^(2) + 6x + 8y + 24 = 0` is `(3sqrt(3))/(4)`.
STATEMENT-2 : The abscissae of two points A and B are the roots of the equation `x^(2) + 3ax + b^(2) =0` and their ordinates are the roots of `x^(2) + 3bx + a^(2) =0` Then the equation of the circle with AB as diameter is `x^(2) + y^(2) + 3ax + 3by + a^(2) + b^(2) = 0`.
STATEMENT-3 : If the circle `x^(2) + y^(2) + 2gx + 2fx +c =0` always passes through exactly three quadrants not passing through origin then `c gt 0`.

A

T F T

B

T T T

C

F F F

D

F F T

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Knowledge Check

  • The abscisae of A and B are the roots of the equation x ^(2) + 2ax -b ^(2) =0 and their ordinates are the roots of the equation y ^(2) + 2 py -q ^(2) =0. The equation of the circle with AB as diameter is

    A
    `x ^(2) + y^(2) + 2ax + 2py-b ^(2) -q ^(2) =0`
    B
    `x ^(2) + y^(2) + 2ax+ 2py -b ^(2) -q ^(2) =0`
    C
    `x ^(2) + y^(2) + 2ax + 2py + b^(2) + q^(2) =0`
    D
    None of these

  • Area of the equilateral triangle inscribed in the circle x^2+ y^2 -7x 9y +5=0 is

    A
    `155/8 sqrt 3 sq units`
    B
    `165/8 sqrt 3 sq units`
    C
    `175/8 sqrt 3 sq units`
    D
    `185/8 sqrt 3 sq units`

  • The abscissa of two A and B are the roots of the equation x ^(2) - 4x - 6=0 and their ordinates are the roots of x ^(2) + 5x - 4=0. If r is the radius of circle with AB as diameter, then r is equal to

    A
    `9/2`
    B
    `9`
    C
    `7/2`
    D
    `7`

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