The abscissa and ordinates of the endpoints `Aa n dB` of a focal chord of the parabola `y^2=4x` are, respectively, the roots of equations `x^2-3x+a=0` and `y^2+6y+b=0` . Then find the equation of the circle with `A B` as diameter.

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the equation of the directrix.

If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , then find the equation of the circle on A B as diameter.

If y=2x is a chord of the circle x^2+y^2-10 x=0 , find the equation of a circle with this chord as diameter.

The abscissae of two points A and B are the roots of the equaiton x^2 + 2x-a^2 =0 and the ordinats are the roots of the equaiton y^2 + 4y-b^2 =0 . Find the equation of the circle with AB as its diameter. Also find the coordinates of the centre and the length of the radius of the circle.

The abscissa of the two points A and B are the roots of the equation x^2+2a x-b^2=0 and their ordinates are the roots of the equation x^2+2p x-q^2=0. Find the equation of the circle with AB as diameter. Also, find its radius.

The abscissa of the two points A and B are the roots of the equation x^2+2a x-b^2=0 and their ordinates are the roots of the equation x^2+2p x-q^2=0. Find the equation of the circle with AB as diameter. Also, find its radius.

If the abscissa and ordinates of two points Pa n dQ are the roots of the equations x^2+2a x-b^2=0 and x^2+2p x-q^2=0 , respectively, then find the equation of the circle with P Q as diameter.

If the abscissa and ordinates of two points Pa n dQ are the roots of the equations x^2+2a x-b^2=0 and x^2+2p x-q^2=0 , respectively, then find the equation of the circle with P Q as diameter.