If `(x_(1),y_(1))` and `(x_(2),y_(2))` are the ends of a focal chord of the parabola `y^(2)` = 4ax then show that `x_(1)x_(2)=a^(2),y_(1)y_(2)= -4a^(2)`

If (x_(1),y_(1)) and (x_(2),y_(2)) are ends of focal chord of y^(2)=4ax then x_(1)x_(2)+y_(1)y_(2) =

If x-2y-a=0 is a chord of the parabola y^(2)=4ax , then its langth, is

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

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

The locus of the middle points of the focal chords of the parabola, y 2 =4x

The slopes of the focal chords of the parabola y^(2)=32 x which are tangents to the circle x^(2)+y^(2)-4 are

Show that the equation of the chord joining two points (x_(1),y_(1)) and (x_(2),y_(2)) on the rectangular hyperbola xy=c^(2) is (x)/(x_(1)+x_(2)) +(y)/(y_(1)+y_(2))=1

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.

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.

If t_(1),t_(2),t_(3) are the feet of normals drawn from (x_(1),y_(1)) to the parabola y^(2)=4ax then the value of t_(1)t_(2)t_(3) =