The locus of the middle points of the focal chords of the parabola, `y^2=4x` is:

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

Find the equation of the locus of the middle points of the chords of the hyperbola 2x^2-3y^2=1, each of which makes an angle of 45^0 with the x-axis.

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

Find the locus of the midpoint of normal chord of parabola y^2=4ax

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

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.

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 .

Find the locus of the point of intersection of the normals at the end of the focal chord of the parabola y^2=4a xdot

The locus of mid-points of a focal chord of the ellipse x^2/a^2+y^2/b^2=1

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is x+y=2 (b) x-y=2 2x-y=1 (d) none of these