If `A_1B_1` and `A_2B_2` are two focal chords of the parabola `y^2=4a x ,` then the chords `A_1A_2` and `B_1B_2` intersect on (a)directrix (b) axis (c)tangent at vertex (d) none of these

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

If aa n dc are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a)real and distinct (b) real and equal (c)imaginary (d) none of these

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

If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , then the length of S Q is (a)6 (b) 4 (c) 3 (d) none of these

Length of the focal chord of the parabola (y +3)^(2) = -8(x-1) which lies at a distance 2 units from the vertex of the parabola is

The point of intersection of the tangents of the parabola y^(2)=4x drawn at the end point of the chord x+y=2 lies on

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x, then prove that 2a=b^2

t 1 and  t 2 are two points on the parabola y^2 =4ax . If the focal chord joining them coincides with the normal chord, then  (a) t1(t1+t2)+2=0 (b) t1+t2=0 (c) t1*t2=-1 (d) none of these     

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4(x+1), then prove that 2(a+1)=b^2

AB and CD are two equal and parallel chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 . Tangents to the ellipse at A and B intersect at P and tangents at C and D at Q. The line PQ