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.

If (t^(2),2t) is one end ofa focal chord of the parabola,y^(2)=4x then the length of the focal chord will be:

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

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

If P(2, 1) is one end of focal chord PQ of the parabola x^(2)+2y- 2x-2=0 then the slope of the normal at Q is

If P(-3, 2) is one end of the focal chord PQ of the parabola y^(2) + 4x + 4y = 0 , then the slope of the normal at Q is

If t_(1) and t_(2) are the ends of a focal chord of the parabola y^(2)=4ax, then prove that the roots of the equation t_(1)x^(2)+ax+t_(2)=0 are real.