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

For the parabola y^2 = 8x , write its focus and the equation of the directrix.

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 parametric equation of a parabola is x=t^2+1,y=2t+1. Then find the equation of the directrix.

The directrix of the parabola x^(2)=-4y is ……..

If the line y=3x+c touches the parabola y^2=12 x at point P , then find the equation of the tangent at point Q where P Q is a focal chord.

The focus of the parabola x^2 -2x +8y + 17=0 is :

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

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 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.

Let (2,3) be the focus of a parabola and x + y = 0 and x-y= 0 be its two tangents. Then equation of its directrix will be