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`

IF (a,b) is the mid point of chord passing through the vertex of the parabola y^2=4x , then

If (a,b) is the midpoint of a chord passing through the vertex of the parabola y^(2)=4x then (A) a=2b(B)2a=b(C)a^(2)=2b(D)2a=b^(2)

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

The vertex of the parabola y^(2) =(a-b)(x -a) is

Show that the locus of the mid-points of all chords passing through the vertices of the parabola y^(2) =4ax is the parabola y^(2)=2ax .

Show that the locus of the mid point of chords of a parabola passing through the vertex is a parabola

Let P be the mid-point of a chord joining the vertex of the parabola y^(2)=8x to another point on it.Then,the locus of P is (A)y^(2)=2x (B) y^(2)=4x(C)(y^(2))/(4)+y^(2)=1(D)x^(2)+(y^(2))/(4)=1

Prove that the locus of the middle points of all chords of the parabola y^(2)=4ax passing through the vertex is the parabola y^(2)=2ax