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.

The focal chord of the parabola y^2=a x 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 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.

Length of the shortest normal chord of the parabola y^2=4ax is

Prove that the chord y-xsqrt(2)+4asqrt(2)=0 is a normal chord of the parabola y^2=4a x . Also find the point on the parabola when the given chord is normal to the parabola.

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3dot

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

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

If one end of the a diameter of the circle 2x^2+2y^2-4x-8y+2=0 is (3, 2), then find the other end of the diameter.

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.