Circles are drawn with diameter being any focal chord of the parabola `y^2-4x-y-4=0` with always touch a fixed line. Find its equation.

Circles drawn on the diameter as focal distance of any point lying on the parabola x^(2)-4x+6y+10 =0 will touch a fixed line whose equation is -

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

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

Find the points on the parabola y^2-2y-4x=0 whose focal length is 6.

The length of focal chord to the parabola y^(2)=12x drawn from the point (3,6) on is __________ .

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 (2,-8) is at an end of a focal chord of the parabola y^2=32 x , then find the other end of the chord.

PQ is any focal chord of the parabola y^(2)=8 x. Then the length of PQ can never be less than _________ .

If AFB is a focal chord of the parabola y^(2) = 4ax such that AF = 4 and FB = 5 then the latus-rectum of the parabola is equal to

The equation to the line touching both the parabolas y^2 =4x and x^2=-32y is